{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:32:35Z","timestamp":1760229155777,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,5,31]],"date-time":"2022-05-31T00:00:00Z","timestamp":1653955200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China (NSFC)","doi-asserted-by":"publisher","award":["61871092","15TD0022"],"award-info":[{"award-number":["61871092","15TD0022"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"University Innovation Team Project Fund of the Sichuan Provincial Department of Education","award":["61871092","15TD0022"],"award-info":[{"award-number":["61871092","15TD0022"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In this paper, we propose a computationally efficient algorithm with improved effective aperture for coherent angle estimation in a monostatic multiple-input multiple-output (MIMO) radar. First, the direction matrix of MIMO radar is mapped into a low-dimensional matrix of virtual uniform linear array (ULA). Then, an augmented data expansion matrix with improved effective aperture is obtained by exploiting the Vandermonde-like structure of the low-dimensional direction matrix and radar cross section (RCS) matrix to enlarge the aperture of the array. Next, a unitary transformation is used to transform the augmented matrix into a real value and the approximate signal subspace of the augmented matrix is obtained by the Nystr\u00f6m method, which can reduce the computational complexity. The eigenvectors of the approximate signal subspace are used to reconstruct the matrix for direct decorrelation processing. Finally, direction of arrivals (DOAs) can be estimated faster by utilizing the unitary ESPRIT algorithm since the rotation invariance of the extended reconstruction matrix still exists. The proposed algorithm has a lower total computational complexity, and the estimation accuracy is improved by utilizing real values and enlarging the array aperture for estimation. Several theoretical analyses and simulation results confirm the effectiveness and advantages of the proposed method.<\/jats:p>","DOI":"10.3390\/rs14112646","type":"journal-article","created":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T21:43:42Z","timestamp":1654119822000},"page":"2646","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Nystr\u00f6m-Based Low-Complexity Algorithm with Improved Effective Array Aperture for Coherent DOA Estimation in Monostatic MIMO Radar"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5490-0977","authenticated-orcid":false,"given":"Teng","family":"Ma","sequence":"first","affiliation":[{"name":"Department of Communication Engineering, Chengdu University of Information Technology, Chengdu 610225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiang","family":"Du","sequence":"additional","affiliation":[{"name":"Department of Communication Engineering, Chengdu University of Information Technology, Chengdu 610225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huaizong","family":"Shao","sequence":"additional","affiliation":[{"name":"Department of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,31]]},"reference":[{"key":"ref_1","unstructured":"Fishler, E., Haimovich, A., Blum, R., Chizhik, D., Cimini, L., and Valenzuela, R.A. (2004, January 29). MIMO Radar: An Idea Whose Time Has Come. Proceedings of the 2004 IEEE Radar Conference, Philadelphia, PA, USA."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"968","DOI":"10.1109\/LSP.2007.905051","article-title":"On parameter identifiability of MIMO radar","volume":"14","author":"Li","year":"2007","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1109\/MSP.2007.904812","article-title":"MIMO radar with colocated antennas","volume":"24","author":"Li","year":"2007","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1109\/MSP.2008.4408448","article-title":"MIMO radar with widely separated antennas","volume":"25","author":"Haimovich","year":"2008","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_5","first-page":"144","article-title":"Overview on the target angle estimation technologies for MIMO radar","volume":"19","author":"Zhai","year":"2021","journal-title":"Radar Sci. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"283483","DOI":"10.1155\/2008\/283483","article-title":"Multitarget identification and localization using bistatic MIMO radar systems","volume":"2008","author":"Yan","year":"2007","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1109\/LCOMM.2010.102610.101581","article-title":"Direction of departure (DOD) and direction of arrival (DOA) estimation in MIMO radar with reduced-dimension MUSIC","volume":"14","author":"Zhang","year":"2010","journal-title":"IEEE Commun. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1422","DOI":"10.1049\/el:20089089","article-title":"Angle estimation using ESPRIT without pairing in MIMO radar","volume":"44","author":"Jinli","year":"2008","journal-title":"Electron. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1049\/el:20080276","article-title":"Angle estimation using ESPRIT in MIMO radar","volume":"44","author":"Duofang","year":"2008","journal-title":"Electron. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11432-014-5251-0","article-title":"Cross-correlation matrix Root-MUSIC algorithm for bistatic multiple-input multiple-output radar","volume":"58","author":"Qin","year":"2015","journal-title":"Sci. China Inf. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1007\/s00034-013-9653-9","article-title":"Unitary subspace-based method for angle estimation in bistatic MIMO radar","volume":"33","author":"Li","year":"2014","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1499","DOI":"10.1080\/00207217.2012.751319","article-title":"DOA estimation for monostatic MIMO radar based on unitary root-MUSIC","volume":"100","author":"Wang","year":"2013","journal-title":"Int. J. Electron."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1349","DOI":"10.1016\/j.sigpro.2012.11.011","article-title":"Maximum likelihood estimation of DOD and DOA for bistatic MIMO radar","volume":"93","author":"Tang","year":"2013","journal-title":"Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.dsp.2019.07.014","article-title":"Adaptive filtering algorithm for direction-of-arrival (DOA) estimation with small snapshots","volume":"94","author":"Liu","year":"2019","journal-title":"Digit. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1109\/JSTSP.2021.3061937","article-title":"Tensor decompositions in wireless communications and MIMO radar","volume":"15","author":"Chen","year":"2021","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"99907","DOI":"10.1109\/ACCESS.2019.2930531","article-title":"Off-grid DOA estimation for colocated MIMO radar via reduced-complexity sparse Bayesian learning","volume":"7","author":"Liu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1080\/00207217.2012.669706","article-title":"Computationally efficient DOD and DOA estimation for bistatic MIMO radar with propagator method","volume":"99","author":"Zhang","year":"2012","journal-title":"Int. J. Electron."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"148771","DOI":"10.1109\/ACCESS.2019.2943167","article-title":"An improved propagator estimator for DOA estimation in monostatic MIMO radar in the presence of imperfect waveforms","volume":"7","author":"Shen","year":"2019","journal-title":"IEEE Access"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"8515606","DOI":"10.1155\/2019\/8515606","article-title":"An improved spatial difference smoothing method based on multistage wiener filtering","volume":"2019","author":"Gong","year":"2019","journal-title":"Math. Probl. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1049\/iet-spr.2017.0033","article-title":"Performance analysis of propagator-based ESPRIT for direction of arrival estimation","volume":"12","author":"Li","year":"2018","journal-title":"IET Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1109\/TPAMI.2004.1262185","article-title":"Spectral grouping using the Nystrom method","volume":"26","author":"Fowlkes","year":"2004","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.sigpro.2013.05.007","article-title":"Computationally efficient ESPRIT algorithm for direction-of-arrival estimation based on Nystr\u00f6m method","volume":"94","author":"Qian","year":"2014","journal-title":"Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1183","DOI":"10.1109\/LCOMM.2020.3048023","article-title":"A new approach to achieve a trade-off between direction-of-arrival estimation performance and computational complexity","volume":"25","author":"Veerendra","year":"2021","journal-title":"IEEE Commun. Lett."},{"key":"ref_24","first-page":"2153","article-title":"On the Nystr\u00f6m method for approximating a Gram matrix for improved kernel-based learning","volume":"6","author":"Drineas","year":"2005","journal-title":"J. Mach. Learn. Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/978-981-10-6571-2_41","article-title":"Angle estimation noncircular source MIMO radar via unitary Nystrom method","volume":"463","author":"Wang","year":"2019","journal-title":"Lect. Notes Electr. Eng."},{"key":"ref_26","first-page":"5584688","article-title":"Computationally efficient unitary ESPRIT algorithm in bistatic MIMO radar","volume":"2021","author":"Liu","year":"2021","journal-title":"Math. Probl. Eng."},{"key":"ref_27","first-page":"258","article-title":"Review for coherent DOA estimation technique","volume":"32","author":"Ye","year":"2017","journal-title":"J. Data Acquis. Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3635","DOI":"10.1109\/TSP.2020.2994514","article-title":"An enhanced spatial smoothing technique with ESPRIT algorithm for direction of arrival estimation in coherent scenarios","volume":"68","author":"Pan","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1803","DOI":"10.1016\/j.sigpro.2011.02.004","article-title":"An ESPRIT-like algorithm for coherent DOA estimation based on data matrix decomposition in MIMO radar","volume":"91","author":"Li","year":"2011","journal-title":"Signal Process."},{"key":"ref_30","first-page":"6631196","article-title":"Two-dimensional DOA estimation of MIMO radar coherent source based on Toeplitz matrix set reconstruction","volume":"2021","author":"Zhang","year":"2021","journal-title":"Secur. Commun. Netw."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1080\/00207217.2012.687186","article-title":"Coherent angle estimation based on Hankel matrix construction in bistatic MIMO radar","volume":"100","author":"Zheng","year":"2013","journal-title":"Int. J. Electron."},{"key":"ref_32","unstructured":"Tabrikian, J., and Bekkerman, I. (2005, January 23). Transmission Diversity Smoothing for Multi-Target Localization. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Philadelphia, PA, USA."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1080\/00207217.2014.942804","article-title":"Joint angle and Doppler frequency estimation of coherent targets in monostatic MIMO radar","volume":"102","author":"Cao","year":"2015","journal-title":"Int. J. Electron."},{"key":"ref_34","first-page":"826","article-title":"Computation efficient joint angle and doppler frequency estimation of coherent targets in monostatic MIMO radar","volume":"33","author":"Cao","year":"2018","journal-title":"J. Data Acquis. Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1109\/JSTSP.2013.2285520","article-title":"Joint transmission and reception diversity smoothing for direction finding of coherent targets in MIMO radar","volume":"8","author":"Zhang","year":"2014","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_36","first-page":"1129","article-title":"Joint DOD and DOA estimation for MIMO radar with lower snapshots","volume":"35","author":"Wang","year":"2014","journal-title":"J. Harbin Eng. Univ."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.sigpro.2014.09.037","article-title":"Spatial difference smoothing for coherent sources location in MIMO radar","volume":"109","author":"Hong","year":"2015","journal-title":"Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.1080\/00207217.2018.1440433","article-title":"Smoothing matrix set-based MIMO radar coherent source localization","volume":"105","author":"Shi","year":"2018","journal-title":"Int. J. Electron."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1121\/1.4883360","article-title":"Compressive beamforming","volume":"136","author":"Xenaki","year":"2014","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"18451","DOI":"10.1109\/ACCESS.2017.2749404","article-title":"A tensor-based covariance differencing method for direction estimation in bistatic MIMO radar with unknown spatial colored noise","volume":"5","author":"Wen","year":"2017","journal-title":"IEEE Access"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1109\/LSP.2009.2017573","article-title":"Single snapshot spatial smoothing with improved effective array aperture","volume":"16","author":"Thakre","year":"2009","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"6271648","DOI":"10.1155\/2016\/6271648","article-title":"Transmit\/Receive spatial smoothing with improved effective array aperture for angle and mutual coupling estimation in bistatic MIMO Radar","volume":"2016","author":"Liu","year":"2016","journal-title":"Int. J. Antennas Propag."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Ma, T., Du, J., and Qiao, L.Y. (2021, January 17\u201319). A Low-Complexity DOA Estimation Algorithm Based on Nystr\u00f6m Method for Mixed Signals. Proceedings of the 2021 IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC), Xi\u2019an, China.","DOI":"10.1109\/ICSPCC52875.2021.9564504"},{"key":"ref_44","first-page":"2434","article-title":"Low-complexity root-MUSIC algorithm for angle estimation in monostatic MIMO radar","volume":"39","author":"Xu","year":"2017","journal-title":"Syst. Eng. Electron."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/11\/2646\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:23:08Z","timestamp":1760138588000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/11\/2646"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,31]]},"references-count":44,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["rs14112646"],"URL":"https:\/\/doi.org\/10.3390\/rs14112646","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2022,5,31]]}}}