{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T04:29:38Z","timestamp":1772166578685,"version":"3.50.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,10,7]],"date-time":"2020-10-07T00:00:00Z","timestamp":1602028800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,10,7]],"date-time":"2020-10-07T00:00:00Z","timestamp":1602028800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2017YFB0102501"],"award-info":[{"award-number":["2017YFB0102501"]}]},{"DOI":"10.13039\/501100006606","name":"Natural Science Foundation of Tianjin City","doi-asserted-by":"publisher","award":["18JCQNJC01500"],"award-info":[{"award-number":["18JCQNJC01500"]}],"id":[{"id":"10.13039\/501100006606","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Scientific Research Program of Tianjin Municipal Education Committee","award":["JWK1609"],"award-info":[{"award-number":["JWK1609"]}]},{"name":"Artificial intelligence Science and Technology Support planning Major project of Tianjin","award":["17ZXRGGX00070"],"award-info":[{"award-number":["17ZXRGGX00070"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Wireless Com Network"],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    A novel Toeplitz fourth-order cumulant (FOC) orthonormal propagator rooting method (TFOC\u2009\u2010\u2009OPRM) of direction-of-arrival (DOA) estimation for uniform linear array (\n                    <jats:italic>ULA<\/jats:italic>\n                    ) is proposed in this paper. Specifically, the modified (i.e., reduced-dimension)\n                    <jats:italic>FOC<\/jats:italic>\n                    \u2009\u2009(\n                    <jats:italic>MFOC<\/jats:italic>\n                    ) matrix is achieved at first via removing the redundant information encompassed in the primary\n                    <jats:italic>FOC<\/jats:italic>\n                    matrix; then, the\n                    <jats:italic>TFOC<\/jats:italic>\n                    matrix which possesses Toeplitz structure can be recovered by utilizing the Toeplitz approximation method. To reduce the computational complexity, an effective method based on the polynomial rooting technology is adopted. Finally, the DOAs of incident signals can be estimated by exploiting orthonormal propagator rooting method. The theoretical analysis coupled with simulation results show that the proposed resultant algorithm can reduce the computational complexity significantly, as well as improve the estimation performance in both spatially white noise environment and spatially color noise environment.\n                  <\/jats:p>","DOI":"10.1186\/s13638-020-01806-1","type":"journal-article","created":{"date-parts":[[2020,10,7]],"date-time":"2020-10-07T05:06:17Z","timestamp":1602047177000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A fourth-order cumulant orthonormal propagator rooting method based on Toeplitz approximation"],"prefix":"10.1186","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8494-9613","authenticated-orcid":false,"given":"Heping","family":"Shi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ning","family":"Ma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiwei","family":"Guan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lizhu","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shan","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,10,7]]},"reference":[{"issue":"4","key":"1806_CR1","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1109\/79.526899","volume":"13","author":"H Krim","year":"1996","unstructured":"H. Krim, M. Viberg, Two decades of array signal processing research: The parametric approach. IEEE Signal Process. Mag. 13(4), 67\u201394 (1996)","journal-title":"IEEE Signal Process. Mag."},{"issue":"6","key":"1806_CR2","doi-asserted-by":"publisher","first-page":"1037","DOI":"10.1109\/LCOMM.2019.2911285","volume":"23","author":"F Wen","year":"2019","unstructured":"F. Wen, Computationally efficient DOA estimation algorithm for MIMO radar with imperfect waveforms. IEEE Commun. Lett. 23(6), 1037\u20131040 (2019)","journal-title":"IEEE Commun. Lett."},{"issue":"10","key":"1806_CR3","doi-asserted-by":"publisher","first-page":"2685","DOI":"10.1109\/TSP.2018.2811746","volume":"66","author":"E Claudio","year":"2018","unstructured":"E. Claudio, R. Parisi, G. Jacovitti, Space time MUSIC: Consistent signal subspace estimation for wideband sensor arrays. IEEE Trans. Signal Process. 66(10), 2685\u20132699 (2018)","journal-title":"IEEE Trans. Signal Process."},{"issue":"11","key":"1806_CR4","doi-asserted-by":"publisher","first-page":"1981","DOI":"10.1109\/LCOMM.2019.2939245","volume":"23","author":"X Dai","year":"2019","unstructured":"X. Dai, X. Zhang, Y. Wang, Extended DOA-matrix method for DOA estimation via two parallel linear arrays. IEEE Commun. Lett. 23(11), 1981\u20131984 (2019)","journal-title":"IEEE Commun. Lett."},{"issue":"3","key":"1806_CR5","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1109\/TAP.1986.1143830","volume":"34","author":"R Schmidt","year":"1986","unstructured":"R. Schmidt, Multiple emitter location and signal parameter estimation. IEEE Trans. Antennas Propag. 34(3), 276\u2013280 (1986)","journal-title":"IEEE Trans. Antennas Propag."},{"issue":"7","key":"1806_CR6","doi-asserted-by":"publisher","first-page":"984","DOI":"10.1109\/29.32276","volume":"37","author":"R Roy","year":"1989","unstructured":"R. Roy, T. Kailath, ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Trans. Acoust. Speech Signal Process. 37(7), 984\u2013995 (1989)","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"issue":"11","key":"1806_CR7","doi-asserted-by":"publisher","first-page":"4104","DOI":"10.1109\/TSP.2005.857012","volume":"53","author":"Z Shan","year":"2005","unstructured":"Z. Shan, T.P. Yum, A conjugate augmented approach to direction-of-arrival estimation. IEEE Trans. Signal Process. 53(11), 4104\u20134109 (2005)","journal-title":"IEEE Trans. Signal Process."},{"issue":"3","key":"1806_CR8","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1109\/LSP.2008.2010816","volume":"16","author":"W Zeng","year":"2009","unstructured":"W. Zeng, X. Li, X. Zhang, Direction-of-arrival estimation based on the joint diagonalization structure of multiple fourth-order cumulant matrices. IEEE Signal Processing Letters 16(3), 164\u2013167 (2009)","journal-title":"IEEE Signal Processing Letters"},{"issue":"2","key":"1806_CR9","doi-asserted-by":"publisher","first-page":"956","DOI":"10.1109\/TAES.2019.2921194","volume":"56","author":"J He","year":"2020","unstructured":"J. He, Z. Zhang, C. Gu, T. Shu, W. Yu, Cumulant-based 2-D direction estimation using an acoustic vector sensor array. IEEE Trans. Aerosp. Electron. Syst. 56(2), 956\u2013971 (2020)","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"1806_CR10","doi-asserted-by":"crossref","unstructured":"B. Liao, S. Chan, A cumulant-based method for direction finding in uniform linear arrays with mutual coupling. IEEE Antennas Wireless Propagation Letters 13, 1717, 2014\u20131720","DOI":"10.1109\/LAWP.2014.2352939"},{"issue":"4","key":"1806_CR11","doi-asserted-by":"publisher","first-page":"1254","DOI":"10.1109\/TSP.2005.843703","volume":"53","author":"P Chevalier","year":"2005","unstructured":"P. Chevalier, L. Albera, A. Ferreol, P. Comon, On the virtual array concept for higher order array processing. IEEE Trans. Signal Process. 53(4), 1254\u20131271 (2005)","journal-title":"IEEE Trans. Signal Process."},{"key":"1806_CR12","doi-asserted-by":"crossref","unstructured":"S. Marcos, A. Marsal and M. Benidir, \u201cPerformances analysis of the propagator method for source bearing estimation,\u201d IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Adelaide, SA, 1994.","DOI":"10.1016\/0165-1684(94)00122-G"},{"issue":"2","key":"1806_CR13","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1016\/0165-1684(94)00122-G","volume":"42","author":"S Marcos","year":"1995","unstructured":"S. Marcos, A. Marsal, M. Benidir, The propagator method for source bearing estimation. Signal Process. 42(2), 121\u2013138 (1995)","journal-title":"Signal Process."},{"key":"1806_CR14","doi-asserted-by":"crossref","unstructured":"L. An and W. Shu, \u201cPropagator method for DOA estimation using fourth-order cumulant,\u201d 2011 7th International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM), Wuhan, 1-4, 2011.","DOI":"10.1109\/wicom.2011.6039941"},{"key":"1806_CR15","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1109\/LAWP.2009.2015224","volume":"8","author":"J He","year":"2009","unstructured":"J. He, Z. Liu, Extended aperture 2-D direction finding with a two-parallel-shape-array using propagator method. IEEE Antennas Wireless Propagation Letters 8, 323\u2013327 (2009)","journal-title":"IEEE Antennas Wireless Propagation Letters"},{"issue":"3","key":"1806_CR16","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1109\/LCOMM.2019.2960341","volume":"24","author":"T Ahmed","year":"2020","unstructured":"T. Ahmed, X. Zhang, W.U. Hassan, A higher-order propagator method for 2D-DOA estimation in massive MIMO systems. IEEE Commun. Lett. 24(3), 543\u2013547 (2020)","journal-title":"IEEE Commun. Lett."},{"key":"1806_CR17","doi-asserted-by":"publisher","first-page":"83","DOI":"10.2528\/PIERB09081806","volume":"18","author":"P Palanisamy","year":"2009","unstructured":"P. Palanisamy, N. Rao, Direction of arrival estimation based on fourth-order cumulant using propagator method. Prog Electromagnetics Res B 18, 83\u201399 (2009)","journal-title":"Prog Electromagnetics Res B"},{"issue":"6","key":"1806_CR18","first-page":"88","volume":"43","author":"J Tang","year":"2009","unstructured":"J. Tang, X. Si, Q. Peng, Estimation of signal parameters via rotational invariance techniques algorithm with speedy fourth-order cumulants. J. Xi'an Jiaotong Univ. 43(6), 88\u201392 (2009)","journal-title":"J. Xi'an Jiaotong Univ."},{"issue":"18","key":"1806_CR19","doi-asserted-by":"publisher","first-page":"1277","DOI":"10.1049\/el.2017.2292","volume":"53","author":"D Zhang","year":"2017","unstructured":"D. Zhang, Y. Zhang, G. Zheng, C. Feng, J. Tang, Improved DOA estimation algorithm for co-prime linear arrays using root-MUSIC algorithm. Electron. Lett. 53(18), 1277\u20131279 (2017)","journal-title":"Electron. Lett."},{"issue":"5","key":"1806_CR20","doi-asserted-by":"publisher","first-page":"1923","DOI":"10.1109\/TSP.2005.845489","volume":"53","author":"J Selva","year":"2005","unstructured":"J. Selva, Computation of spectral and root MUSIC through real polynomial rooting. IEEE Trans. Signal Process. 53(5), 1923\u20131927 (2005)","journal-title":"IEEE Trans. Signal Process."},{"issue":"21","key":"1806_CR21","doi-asserted-by":"crossref","first-page":"7792","DOI":"10.1049\/joe.2019.0735","volume":"2019","author":"X Meng","year":"2019","unstructured":"X. Meng, J. Xue, F. Yan, X. Yan, Real-valued propagator method for fast DOA estimation via polynomial rooting. J Eng 2019(21), 7792\u20137795 (2019)","journal-title":"J Eng"},{"key":"1806_CR22","doi-asserted-by":"publisher","first-page":"122330","DOI":"10.1109\/ACCESS.2019.2938538","volume":"7","author":"F Yan","year":"2019","unstructured":"F. Yan, X. Li, T. Jin, L. Liu, M. Jin, A real-valued polynomial rooting method for fast direction of arrival estimation with large uniform linear arrays. IEEE Access 7, 122330\u2013122341 (2019)","journal-title":"IEEE Access"},{"issue":"3","key":"1806_CR23","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1109\/MAP.2003.1232160","volume":"45","author":"SR Best","year":"2003","unstructured":"S.R. Best, A discussion on the significance of geometry in determining the resonant behavior of fractal and other non-Euclidean wire antennas. IEEE Antennas Propagation Magazine 45(3), 9\u201328 (2003)","journal-title":"IEEE Antennas Propagation Magazine"},{"issue":"3","key":"1806_CR24","doi-asserted-by":"publisher","first-page":"84","DOI":"10.3390\/e18030084","volume":"18","author":"E Guariglia","year":"2016","unstructured":"E. Guariglia, Entropy and fractal antennas. Entropy 18(3), 84 (2016)","journal-title":"Entropy"},{"key":"1806_CR25","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1109\/LAWP.2002.802584","volume":"1","author":"SR Best","year":"2002","unstructured":"S.R. Best, Operating band comparison of the perturbed Sierpinski and modified Parany gasket antennas. IEEE Antennas Wireless Propagation Letters 1, 35\u201338 (2002)","journal-title":"IEEE Antennas Wireless Propagation Letters"},{"issue":"9","key":"1806_CR26","doi-asserted-by":"publisher","first-page":"714","DOI":"10.3390\/e20090714","volume":"20","author":"E Guariglia","year":"2018","unstructured":"E. Guariglia, Harmonic Sierpinski gasket and applications. Entropy 20(9), 714 (2018)","journal-title":"Entropy"},{"issue":"2","key":"1806_CR27","first-page":"3","volume":"19","author":"WJ Krzysztofik","year":"2013","unstructured":"W.J. Krzysztofik, Fractal geometry in electromagnetics applications-from antenna to metamaterials. Microwave Rev 19(2), 3\u201314 (2013)","journal-title":"Microwave Rev"},{"key":"1806_CR28","doi-asserted-by":"crossref","unstructured":"R.G. Hohlfeld, N. Cohen, Self-similarity and the geometric requirements for frequency independence in antennae. Fractals-complex Geometry Patterns & Scaling in Nature & Society 7(01), 79\u201384 (1999)","DOI":"10.1142\/S0218348X99000098"},{"key":"1806_CR29","unstructured":"E. Guariglia, \u201cSpectral analysis of the Weierstrass-Mandelbrot function,\u201d 2017 2nd International Multidisciplinary Conference on Computer and Energy Science (SpliTech), Split, pp. 1-6, 2017."},{"key":"1806_CR30","first-page":"337","volume-title":"Engineering Mathematics II, Springer Proceedings in Mathematics & Statistics","author":"E Guariglia","year":"2016","unstructured":"E. Guariglia, S. Silvestrov, in Engineering Mathematics II, Springer Proceedings in Mathematics & Statistics, ed. by S. Silvestrov, M. Ran\u010di\u0107. Fractional-wavelet analysis of positive definite distributions and wavelets on D'(C), vol 179 (2016), pp. 337\u2013353"},{"issue":"9","key":"1806_CR31","doi-asserted-by":"publisher","first-page":"2592","DOI":"10.1109\/78.782217","volume":"47","author":"P Chevalier","year":"1999","unstructured":"P. Chevalier, A. Ferreol, On the virtual array concept for the fourth-order direction finding problem. IEEE Trans. Signal Process. 47(9), 2592\u20132595 (1999)","journal-title":"IEEE Trans. Signal Process."},{"key":"1806_CR32","doi-asserted-by":"crossref","unstructured":"A. J. Barabell, \u201cImproving the resolution performance of eigen-structure-based direction-finding algorithms,\u201d Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., Boston, MA, USA, May, 336-339, 1983.","DOI":"10.1109\/ICASSP.1983.1172124"},{"issue":"12","key":"1806_CR33","doi-asserted-by":"publisher","first-page":"1939","DOI":"10.1109\/29.45540","volume":"37","author":"B Rao","year":"1989","unstructured":"B. Rao, K. Hari, Performance analysis of root-MUSIC. IEEE Trans. Acoust. Speech Signal Process. 37(12), 1939\u20131949 (1989)","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"issue":"6","key":"1806_CR34","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1049\/el:19970272","volume":"33","author":"Q Ren","year":"1997","unstructured":"Q. Ren, A. Willis, Fast root MUSIC algorithm. Electron. Lett. 33(6), 450\u2013451 (1997)","journal-title":"Electron. Lett."}],"container-title":["EURASIP Journal on Wireless Communications and Networking"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13638-020-01806-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s13638-020-01806-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13638-020-01806-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,15]],"date-time":"2024-08-15T12:36:46Z","timestamp":1723725406000},"score":1,"resource":{"primary":{"URL":"https:\/\/jwcn-eurasipjournals.springeropen.com\/articles\/10.1186\/s13638-020-01806-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,7]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["1806"],"URL":"https:\/\/doi.org\/10.1186\/s13638-020-01806-1","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-30333\/v1","asserted-by":"object"},{"id-type":"doi","id":"10.21203\/rs.3.rs-30333\/v2","asserted-by":"object"}]},"ISSN":["1687-1499"],"issn-type":[{"value":"1687-1499","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,7]]},"assertion":[{"value":"2 June 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 September 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 October 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"The authors declare that they have no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"193"}}