Complex Elliptically Symmetric Distributions: Survey, New Results and Applications
Complex elliptically symmetric (CES) distributions have been widely used in various engineering applications for which non-Gaussian models are needed. In this overview, circular CES distributions are surveyed, some new results are derived and their applications e.g., in radar and array signal proces...
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| Veröffentlicht in: | IEEE transactions on signal processing 2012-11, Vol.60 (11), p.5597-5625 |
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| container_title | IEEE transactions on signal processing |
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| creator | Ollila, E. Tyler, D. E. Koivunen, V. Poor, H. V. |
| description | Complex elliptically symmetric (CES) distributions have been widely used in various engineering applications for which non-Gaussian models are needed. In this overview, circular CES distributions are surveyed, some new results are derived and their applications e.g., in radar and array signal processing are discussed and illustrated with theoretical examples, simulations and analysis of real radar data. The maximum likelihood (ML) estimator of the scatter matrix parameter is derived and general conditions for its existence and uniqueness, and for convergence of the iterative fixed point algorithm are established. Specific ML-estimators for several CES distributions that are widely used in the signal processing literature are discussed in depth, including the complex t -distribution, K -distribution, the generalized Gaussian distribution and the closely related angular central Gaussian distribution. A generalization of ML-estimators, the M -estimators of the scatter matrix, are also discussed and asymptotic analysis is provided. Applications of CES distributions and the adaptive signal processors based on ML- and M -estimators of the scatter matrix are illustrated in radar detection problems and in array signal processing applications for Direction-of-Arrival (DOA) estimation and beamforming. Furthermore, experimental validation of the usefulness of CES distributions for modelling real radar data is given. |
| doi_str_mv | 10.1109/TSP.2012.2212433 |
| format | Article |
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E. ; Koivunen, V. ; Poor, H. V.</creator><creatorcontrib>Ollila, E. ; Tyler, D. E. ; Koivunen, V. ; Poor, H. V.</creatorcontrib><description>Complex elliptically symmetric (CES) distributions have been widely used in various engineering applications for which non-Gaussian models are needed. In this overview, circular CES distributions are surveyed, some new results are derived and their applications e.g., in radar and array signal processing are discussed and illustrated with theoretical examples, simulations and analysis of real radar data. The maximum likelihood (ML) estimator of the scatter matrix parameter is derived and general conditions for its existence and uniqueness, and for convergence of the iterative fixed point algorithm are established. Specific ML-estimators for several CES distributions that are widely used in the signal processing literature are discussed in depth, including the complex t -distribution, K -distribution, the generalized Gaussian distribution and the closely related angular central Gaussian distribution. A generalization of ML-estimators, the M -estimators of the scatter matrix, are also discussed and asymptotic analysis is provided. Applications of CES distributions and the adaptive signal processors based on ML- and M -estimators of the scatter matrix are illustrated in radar detection problems and in array signal processing applications for Direction-of-Arrival (DOA) estimation and beamforming. 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E.</creatorcontrib><creatorcontrib>Koivunen, V.</creatorcontrib><creatorcontrib>Poor, H. V.</creatorcontrib><title>Complex Elliptically Symmetric Distributions: Survey, New Results and Applications</title><title>IEEE transactions on signal processing</title><addtitle>TSP</addtitle><description>Complex elliptically symmetric (CES) distributions have been widely used in various engineering applications for which non-Gaussian models are needed. In this overview, circular CES distributions are surveyed, some new results are derived and their applications e.g., in radar and array signal processing are discussed and illustrated with theoretical examples, simulations and analysis of real radar data. The maximum likelihood (ML) estimator of the scatter matrix parameter is derived and general conditions for its existence and uniqueness, and for convergence of the iterative fixed point algorithm are established. Specific ML-estimators for several CES distributions that are widely used in the signal processing literature are discussed in depth, including the complex t -distribution, K -distribution, the generalized Gaussian distribution and the closely related angular central Gaussian distribution. A generalization of ML-estimators, the M -estimators of the scatter matrix, are also discussed and asymptotic analysis is provided. Applications of CES distributions and the adaptive signal processors based on ML- and M -estimators of the scatter matrix are illustrated in radar detection problems and in array signal processing applications for Direction-of-Arrival (DOA) estimation and beamforming. Furthermore, experimental validation of the usefulness of CES distributions for modelling real radar data is given.</description><subject>Adaptive signal processing</subject><subject>Algorithms</subject><subject>Analytical models</subject><subject>Applied sciences</subject><subject>array processing</subject><subject>Arrays</subject><subject>Asymptotic properties</subject><subject>CFAR</subject><subject>complex elliptical distributions</subject><subject>Covariance matrix</subject><subject>detection</subject><subject>Detection, estimation, filtering, equalization, prediction</subject><subject>distribution-freeness</subject><subject>Exact sciences and technology</subject><subject>Information, signal and communications theory</subject><subject>M -estimation</subject><subject>Miscellaneous</subject><subject>ML-estimation</subject><subject>Noise</subject><subject>Normal distribution</subject><subject>Program processors</subject><subject>Radar</subject><subject>Radar data</subject><subject>Radar detection</subject><subject>Robustness</subject><subject>Scatter</subject><subject>Signal and communications theory</subject><subject>Signal processing</subject><subject>Signal, noise</subject><subject>Studies</subject><subject>Telecommunications and information theory</subject><issn>1053-587X</issn><issn>1941-0476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkM1rGzEQxZfSQlO390AvCyHQQ9bRSFpplZtx81EIabET6E3I8izIaD8i7abxf185Nj7k9Abm994ML8tOgUwBiLp8XP6ZUgJ0SilQztiH7AQUh4JwKT6mmZSsKCv593P2JcYNIcC5EifZYt41vcfX_Np71w_OGu-3-XLbNDgEZ_OfLiZdjYPr2niVL8fwgtuL_AH_5QuMox9ibtp1Put7n7xv1NfsU218xG8HnWRPN9eP87vi_vftr_nsvrBcyKFgddIKZW1kGtdWlrhSdYU1KxUj1irJwcKqUqKU3GBZQsUEsnWlFGUcKJtkP_a5feieR4yDbly06L1psRujBiZK4DSFJfTsHbrpxtCm7zQAUGAsHUsU2VM2dDEGrHUfXGPCVgPRu5J1KlnvStaHkpPl_BBsYqquDqa1Lh59VEiVPuWJ-77nHCIe14IKxtLx_1DihGE</recordid><startdate>20121101</startdate><enddate>20121101</enddate><creator>Ollila, E.</creator><creator>Tyler, D. 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V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c467t-3fc468e7fa73fcdc75eb9f8ef35930cc9741c1b896574ae551836e3d899234123</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Adaptive signal processing</topic><topic>Algorithms</topic><topic>Analytical models</topic><topic>Applied sciences</topic><topic>array processing</topic><topic>Arrays</topic><topic>Asymptotic properties</topic><topic>CFAR</topic><topic>complex elliptical distributions</topic><topic>Covariance matrix</topic><topic>detection</topic><topic>Detection, estimation, filtering, equalization, prediction</topic><topic>distribution-freeness</topic><topic>Exact sciences and technology</topic><topic>Information, signal and communications theory</topic><topic>M -estimation</topic><topic>Miscellaneous</topic><topic>ML-estimation</topic><topic>Noise</topic><topic>Normal distribution</topic><topic>Program processors</topic><topic>Radar</topic><topic>Radar data</topic><topic>Radar detection</topic><topic>Robustness</topic><topic>Scatter</topic><topic>Signal and communications theory</topic><topic>Signal processing</topic><topic>Signal, noise</topic><topic>Studies</topic><topic>Telecommunications and information theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ollila, E.</creatorcontrib><creatorcontrib>Tyler, D. 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V.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><jtitle>IEEE transactions on signal processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Ollila, E.</au><au>Tyler, D. E.</au><au>Koivunen, V.</au><au>Poor, H. V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Complex Elliptically Symmetric Distributions: Survey, New Results and Applications</atitle><jtitle>IEEE transactions on signal processing</jtitle><stitle>TSP</stitle><date>2012-11-01</date><risdate>2012</risdate><volume>60</volume><issue>11</issue><spage>5597</spage><epage>5625</epage><pages>5597-5625</pages><issn>1053-587X</issn><eissn>1941-0476</eissn><coden>ITPRED</coden><abstract>Complex elliptically symmetric (CES) distributions have been widely used in various engineering applications for which non-Gaussian models are needed. In this overview, circular CES distributions are surveyed, some new results are derived and their applications e.g., in radar and array signal processing are discussed and illustrated with theoretical examples, simulations and analysis of real radar data. The maximum likelihood (ML) estimator of the scatter matrix parameter is derived and general conditions for its existence and uniqueness, and for convergence of the iterative fixed point algorithm are established. Specific ML-estimators for several CES distributions that are widely used in the signal processing literature are discussed in depth, including the complex t -distribution, K -distribution, the generalized Gaussian distribution and the closely related angular central Gaussian distribution. A generalization of ML-estimators, the M -estimators of the scatter matrix, are also discussed and asymptotic analysis is provided. Applications of CES distributions and the adaptive signal processors based on ML- and M -estimators of the scatter matrix are illustrated in radar detection problems and in array signal processing applications for Direction-of-Arrival (DOA) estimation and beamforming. 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| subjects | Adaptive signal processing Algorithms Analytical models Applied sciences array processing Arrays Asymptotic properties CFAR complex elliptical distributions Covariance matrix detection Detection, estimation, filtering, equalization, prediction distribution-freeness Exact sciences and technology Information, signal and communications theory M -estimation Miscellaneous ML-estimation Noise Normal distribution Program processors Radar Radar data Radar detection Robustness Scatter Signal and communications theory Signal processing Signal, noise Studies Telecommunications and information theory |
| title | Complex Elliptically Symmetric Distributions: Survey, New Results and Applications |
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