{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T06:50:04Z","timestamp":1759042204300,"version":"3.37.3"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T00:00:00Z","timestamp":1682899200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T00:00:00Z","timestamp":1682899200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Innovation team of Pu\u2019er University","award":["CXTD019"],"award-info":[{"award-number":["CXTD019"]}]},{"name":"Scientific Research Fund Project of Yunnan Education Department","award":["2022J0985"],"award-info":[{"award-number":["2022J0985"]}]},{"DOI":"10.13039\/501100009329","name":"Guangxi Science and Technology Planning Project","doi-asserted-by":"crossref","award":["2022AC21276"],"award-info":[{"award-number":["2022AC21276"]}],"id":[{"id":"10.13039\/501100009329","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["EURASIP J. Adv. Signal Process."],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper provides a method for enumerating signals impinging on an array of sensors based on the generalized Bayesian information criterion (GBIC). The proposed method motivates by a statistic for testing the sphericity of the covariance matrix when the sample size <jats:italic>n<\/jats:italic> is less than the dimension <jats:italic>m<\/jats:italic>. The statistic consists of the first four moments of sample eigenvalue distribution and relaxes the assumption of Gaussian distribution. We derive the asymptotical distribution of the statistic as <jats:italic>m<\/jats:italic>, <jats:italic>n<\/jats:italic> tends to infinity at the same ratio by random matrix theory and propose the expression of GBIC for determining the signal number. Numerical simulations demonstrate that the proposed method has a high probability of detection in both the Gaussian and the non-Gaussian noise, and performs better than other methods.<\/jats:p>","DOI":"10.1186\/s13634-023-01012-3","type":"journal-article","created":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T11:02:23Z","timestamp":1682938943000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An RMT-based generalized Bayesian information criterion for signal enumeration"],"prefix":"10.1186","volume":"2023","author":[{"given":"Shoucheng","family":"Yuan","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7654-5072","authenticated-orcid":false,"given":"Bin","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,5,1]]},"reference":[{"issue":"7","key":"1012_CR1","doi-asserted-by":"publisher","first-page":"1220","DOI":"10.1049\/iet-rsn.2015.0479","volume":"10","author":"J Morales","year":"2016","unstructured":"J. Morales, S. Agaian, D. Akopian, Mitigating anomalous measurements for indoor wireless local area network positioning. IET Radar Sonar Navig. 10(7), 1220\u20131227 (2016)","journal-title":"IET Radar Sonar Navig."},{"issue":"3","key":"1012_CR2","doi-asserted-by":"publisher","first-page":"927","DOI":"10.1109\/TAES.2008.4655353","volume":"44","author":"L Xu","year":"2008","unstructured":"L. Xu, J. Li, P. Stoica, Target detection and parameter estimation for mimo radar systems. IEEE Trans. Aerosp. Electron. Syst. 44(3), 927\u2013939 (2008)","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"issue":"6","key":"1012_CR3","doi-asserted-by":"publisher","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","volume":"19","author":"H Akaike","year":"1974","unstructured":"H. Akaike, A new look at the statistical model identification. IEEE Trans. Autom. Control 19(6), 716\u2013723 (1974)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"2","key":"1012_CR4","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1214\/aos\/1176344136","volume":"6","author":"G Schwarz","year":"1978","unstructured":"G. Schwarz, Estimating the dimension of a model. Ann. Stat. 6(2), 461\u2013464 (1978)","journal-title":"Ann. Stat."},{"issue":"5","key":"1012_CR5","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1016\/0005-1098(78)90005-5","volume":"14","author":"J Rissanen","year":"1978","unstructured":"J. Rissanen, Modeling by shortest data description. Automatica 14(5), 465\u2013471 (1978)","journal-title":"Automatica"},{"issue":"5","key":"1012_CR6","doi-asserted-by":"publisher","first-page":"1171","DOI":"10.1109\/TSP.2004.826168","volume":"52","author":"S Valaee","year":"2004","unstructured":"S. Valaee, P. Kabal, An information theoretic approach to source enumeration in array signal processing. IEEE Trans. Signal Process. 52(5), 1171\u20131178 (2004)","journal-title":"IEEE Trans. Signal Process."},{"issue":"4","key":"1012_CR7","doi-asserted-by":"publisher","first-page":"1386","DOI":"10.1121\/1.395273","volume":"82","author":"PL Brockett","year":"1987","unstructured":"P.L. Brockett, M. Hinich, G.R. Wilson, Nonlinear and non-Gaussian ocean noise. J. Acoust. Soc. Am. 82(4), 1386\u20131394 (1987)","journal-title":"J. Acoust. Soc. Am."},{"issue":"7","key":"1012_CR8","doi-asserted-by":"publisher","first-page":"991","DOI":"10.1109\/49.233212","volume":"11","author":"KL Blackard","year":"1993","unstructured":"K.L. Blackard, T.S. Rappaport, C.W. Bostian, Measurements and models of radio frequency impulsive noise for indoor wireless communications. IEEE J. Sel. Areas Commun. 11(7), 991\u20131001 (1993)","journal-title":"IEEE J. Sel. Areas Commun."},{"issue":"11","key":"1012_CR9","doi-asserted-by":"publisher","first-page":"5597","DOI":"10.1109\/TSP.2012.2212433","volume":"60","author":"E Ollila","year":"2012","unstructured":"E. Ollila, D.E. Tyler, V. Koivunen, H.V. Poor, Complex elliptically symmetric distributions: survey, new results and applications. IEEE Trans. Signal Process. 60(11), 5597\u20135625 (2012)","journal-title":"IEEE Trans. Signal Process."},{"key":"1012_CR10","unstructured":"H. Asadi, B. Seyfe, Source number estimation via entropy estimation of eigenvalues (EEE) in Gaussian and non-Gaussian noise. arXiv preprint arXiv:1311.6051 (2013)"},{"key":"1012_CR11","unstructured":"G. Anand, P. Nagesha, Source number estimation in non-Gaussian noise. In: IEEE European Signal Processing Conference (EUSIPCO), pp. 1711\u20131715 (2014)"},{"issue":"1","key":"1012_CR12","doi-asserted-by":"publisher","first-page":"494","DOI":"10.1016\/j.aim.2011.02.007","volume":"227","author":"F Benaych-Georges","year":"2011","unstructured":"F. Benaych-Georges, R.R. Nadakuditi, The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices. Adv. Math. 227(1), 494\u2013521 (2011)","journal-title":"Adv. Math."},{"issue":"10","key":"1012_CR13","doi-asserted-by":"publisher","first-page":"3930","DOI":"10.1109\/TSP.2009.2022897","volume":"57","author":"S Kritchman","year":"2009","unstructured":"S. Kritchman, B. Nadler, Non-parametric detection of the number of signals: hypothesis testing and random matrix theory. IEEE Trans. Signal Process. 57(10), 3930\u20133941 (2009)","journal-title":"IEEE Trans. Signal Process."},{"issue":"1","key":"1012_CR14","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1109\/TAES.2014.130579","volume":"51","author":"L Huang","year":"2015","unstructured":"L. Huang, C. Qian, H.C. So, J. Fang, Source enumeration for large array using shrinkage-based detectors with small samples. IEEE Trans. Aerosp. Electron. Syst. 51(1), 344\u2013357 (2015)","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"issue":"5","key":"1012_CR15","doi-asserted-by":"publisher","first-page":"2746","DOI":"10.1109\/TSP.2010.2042481","volume":"58","author":"B Nadler","year":"2010","unstructured":"B. Nadler, Nonparametric detection of signals by information theoretic criteria: performance analysis and an improved estimator. IEEE Trans. Signal Process. 58(5), 2746\u20132756 (2010)","journal-title":"IEEE Trans. Signal Process."},{"issue":"7","key":"1012_CR16","doi-asserted-by":"publisher","first-page":"2625","DOI":"10.1109\/TSP.2008.917356","volume":"56","author":"RR Nadakuditi","year":"2008","unstructured":"R.R. Nadakuditi, A. Edelman, Sample eigenvalue based detection of high-dimensional signals in white noise using relatively few samples. IEEE Trans. Signal Process. 56(7), 2625\u20132638 (2008)","journal-title":"IEEE Trans. Signal Process."},{"issue":"19","key":"1012_CR17","doi-asserted-by":"publisher","first-page":"4806","DOI":"10.1109\/TSP.2013.2273198","volume":"61","author":"L Huang","year":"2013","unstructured":"L. Huang, H.C. So, Source enumeration via MDL criterion based on linear shrinkage estimation of noise subspace covariance matrix. IEEE Trans. Signal Process. 61(19), 4806\u20134821 (2013)","journal-title":"IEEE Trans. Signal Process."},{"issue":"5","key":"1012_CR18","doi-asserted-by":"publisher","first-page":"3018","DOI":"10.1109\/TVT.2015.2436060","volume":"65","author":"L Huang","year":"2016","unstructured":"L. Huang, Y. Xiao, K. Liu, H.C. So, J. Zhang, Bayesian information criterion for source enumeration in large-scale adaptive antenna array. IEEE Trans. Veh. Technol. 65(5), 3018\u20133032 (2016)","journal-title":"IEEE Trans. Veh. Technol."},{"issue":"7","key":"1012_CR19","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1049\/iet-spr.2011.0260","volume":"6","author":"E Yazdian","year":"2012","unstructured":"E. Yazdian, S. Gazor, H. Bastani, Source enumeration in large arrays using moments of eigenvalues and relatively few samples. IET Signal Proc. 6(7), 689\u2013696 (2012)","journal-title":"IET Signal Proc."},{"issue":"6","key":"1012_CR20","doi-asserted-by":"publisher","first-page":"1470","DOI":"10.1109\/TSP.2012.2232661","volume":"61","author":"Z Lu","year":"2013","unstructured":"Z. Lu, A.M. Zoubir, Generalized Bayesian information criterion for source enumeration in array processing. IEEE Trans. Signal Process. 61(6), 1470\u20131480 (2013)","journal-title":"IEEE Trans. Signal Process."},{"issue":"9","key":"1012_CR21","doi-asserted-by":"publisher","first-page":"1333","DOI":"10.1049\/iet-rsn.2016.0581","volume":"11","author":"Y Liu","year":"2017","unstructured":"Y. Liu, X. Sun, S. Zhao, Source enumeration via GBIC with a statistic for sphericity test in white Gaussian and non-Gaussian noise. IET Radar Sonar Navig. 11(9), 1333\u20131339 (2017)","journal-title":"IET Radar Sonar Navig."},{"key":"1012_CR22","doi-asserted-by":"crossref","unstructured":"E. Terreaux, J.-P. Ovarlez, F. Pascal, New model order selection in large dimension regime for complex elliptically symmetric noise. In: IEEE European Signal Processing Conference (EUSIPCO), pp. 1090\u20131094 (2017)","DOI":"10.23919\/EUSIPCO.2017.8081376"},{"key":"1012_CR23","unstructured":"D. Kelker, Distribution theory of spherical distributions and a location-scale parameter generalization. Sankhy\u0101: Indian J. Stat. Ser. A, 419\u2013430 (1970)"},{"key":"1012_CR24","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1214\/aos\/1009210544","volume":"29","author":"IM Johnstone","year":"2001","unstructured":"I.M. Johnstone, On the distribution of the largest eigenvalue in principal components analysis. Ann. Stat. 29, 295\u2013327 (2001)","journal-title":"Ann. Stat."},{"key":"1012_CR25","doi-asserted-by":"publisher","first-page":"2554","DOI":"10.1016\/j.jmva.2010.07.004","volume":"101","author":"TJ Fisher","year":"2010","unstructured":"T.J. Fisher, X. Sun, C.M. Gallagher, A new test for sphericity of the covariance matrix for high dimensional data. J. Multivar. Anal. 101, 2554\u20132570 (2010)","journal-title":"J. Multivar. Anal."},{"key":"1012_CR26","doi-asserted-by":"publisher","first-page":"312","DOI":"10.1016\/j.jspi.2011.07.019","volume":"142","author":"TJ Fisher","year":"2012","unstructured":"T.J. Fisher, On testing for an identity covariance matrix when the dimensionality equals or exceeds the sample size. J. Stat. Plan. Inference 142, 312\u2013326 (2012)","journal-title":"J. Stat. Plan. Inference"},{"key":"1012_CR27","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1016\/j.jmva.2014.06.003","volume":"130","author":"MS Srivastava","year":"2014","unstructured":"M.S. Srivastava, H. Yanagihara, T. Kubokawa, Tests for covariance matrices in high dimension with less sample size. J. Multivar. Anal. 130, 289\u2013309 (2014)","journal-title":"J. Multivar. Anal."},{"key":"1012_CR28","doi-asserted-by":"publisher","first-page":"3822","DOI":"10.1214\/09-AOS694","volume":"37","author":"ZD Bai","year":"2009","unstructured":"Z.D. Bai, D.D. Jiang, J.F. Yao, S.R. Zheng, Corrections to LRT on large-dimensional covariance matrix by RMT. Ann. Stat. 37, 3822\u20133840 (2009)","journal-title":"Ann. Stat."},{"issue":"2","key":"1012_CR29","doi-asserted-by":"publisher","first-page":"251","DOI":"10.14490\/jjss.35.251","volume":"35","author":"MS Srivastava","year":"2005","unstructured":"M.S. Srivastava, Some tests concerning the covariance matrix in high dimensional data. J. Jpn. Stat. Soc. 35(2), 251\u2013272 (2005)","journal-title":"J. Jpn. Stat. Soc."},{"key":"1012_CR30","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/j.jmva.2015.07.010","volume":"141","author":"XT Tian","year":"2015","unstructured":"X.T. Tian, Y.T. Lu, W.M. Li, A robust test for sphericity of high-dimensional covariance matrices. J. Multivar. Anal. 141, 217\u2013227 (2015)","journal-title":"J. Multivar. Anal."}],"container-title":["EURASIP Journal on Advances in Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13634-023-01012-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s13634-023-01012-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13634-023-01012-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T11:04:55Z","timestamp":1682939095000},"score":1,"resource":{"primary":{"URL":"https:\/\/asp-eurasipjournals.springeropen.com\/articles\/10.1186\/s13634-023-01012-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,1]]},"references-count":30,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["1012"],"URL":"https:\/\/doi.org\/10.1186\/s13634-023-01012-3","relation":{},"ISSN":["1687-6180"],"issn-type":[{"type":"electronic","value":"1687-6180"}],"subject":[],"published":{"date-parts":[[2023,5,1]]},"assertion":[{"value":"14 October 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 April 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 May 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The authors declare that they have no competing interests.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"50"}}