{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T12:56:28Z","timestamp":1768740988266,"version":"3.49.0"},"reference-count":43,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,3,16]],"date-time":"2019-03-16T00:00:00Z","timestamp":1552694400000},"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","doi-asserted-by":"publisher","award":["51879221"],"award-info":[{"award-number":["51879221"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Noise suppression capacity in multiple-input multiple-output (MIMO) sonar signal processing is derived under the assumption of white Gaussian noise. However, underwater noise mainly includes white Gaussian noise and colored noise. There exists a certain correlation between the noise signals received by each MIMO sonar array element. The performance of traditional direction-of-arrival (DOA) estimation methods decreases obviously in complex marine noise. In this paper, we propose a marine environment noise suppression method for MIMO applied to multiple targets\u2019 DOA estimation. The noise field can be decomposed into a symmetric noise component and an asymmetric noise component. We use the covariance matrix imaginary component to pre-estimate the signal sources, then use the dimension reduction transformation to reconstruct the real component of the covariance matrix. The Toeplitz technique is utilized to reduce the correlation of the reconstructed covariance matrix. Thus, the subspace decomposition-based techniques such as multiple signal classification (MUSIC) can be used for multiple targets\u2019 DOA estimation. To reduce the computational complexity of the methods, search-free direction-finding techniques such as the estimation of signal parameters via rotational invariance techniques (ESPRIT) can be utilized. As a result, the proposed methods can achieve better direction-finding performance in the condition of limited snapshots with lower computational cost. The corresponding Cramer-Rao bound (CRB) is deduced and the signal-to-noise ratio (SNR) gain obtained by dimension reduction processing is discussed. Simulation results also show the superiority of the proposed method over the existing methods.<\/jats:p>","DOI":"10.3390\/s19061325","type":"journal-article","created":{"date-parts":[[2019,3,18]],"date-time":"2019-03-18T12:18:53Z","timestamp":1552911533000},"page":"1325","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Noise Suppression for Direction of Arrival Estimation in Co-located MIMO Sonar"],"prefix":"10.3390","volume":"19","author":[{"given":"Xue","family":"Cheng","sequence":"first","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingmin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3873","DOI":"10.1109\/TSP.2006.879267","article-title":"Target detection and localization using MIMO radars and sonars","volume":"54","author":"Bekkerman","year":"2006","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1440","DOI":"10.1109\/JSTSP.2015.2467354","article-title":"Optimal Cognitive Beamforming for Target Tracking in MIMO Radar\/Sonar","volume":"9","author":"Sharaga","year":"2015","journal-title":"IEEE J. Sel. Top. Signal Process."},{"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","doi-asserted-by":"crossref","first-page":"5051","DOI":"10.1109\/TSP.2008.928693","article-title":"Diversity-Integration Tradeoffs in MIMO Detection","volume":"56","author":"Maio","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1109\/JSTSP.2009.2038974","article-title":"Target Velocity Estimation and Antenna Placement for MIMO Radar with Widely Separated Antennas","volume":"4","author":"He","year":"2010","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3241","DOI":"10.1109\/TSP.2011.2141665","article-title":"MIMO Radar Sensitivity Analysis for Target Detection","volume":"59","author":"Akcakaya","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2354","DOI":"10.1109\/TSP.2012.2187290","article-title":"Moving Target Parameters Estimation in Noncoherent MIMO Radar Systems","volume":"60","author":"Hassanien","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3683","DOI":"10.1109\/TGRS.2012.2226466","article-title":"Superresolution Multitarget Parameter Estimation in MIMO Radar","volume":"51","author":"Luo","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1539","DOI":"10.1109\/TSP.2010.2100387","article-title":"Performance Bounds and Angular Resolution Limit for the Moving Colocated MIMO Radar","volume":"59","author":"Boyer","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2076","DOI":"10.1109\/TSP.2011.2179540","article-title":"On MIMO Radar Subarrayed Transmit Beamforming","volume":"60","author":"Wilcox","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.1109\/TSP.2012.2234743","article-title":"Receiver Design for Range and Doppler Sidelobe Suppression Using MIMO and Phased-Array Radar","volume":"61","author":"Hua","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3137","DOI":"10.1109\/TSP.2010.2043976","article-title":"Phased-MIMO radar: A tradeoff between phased-array and MIMO radars","volume":"58","author":"Hassanien","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","first-page":"276","article-title":"Frequency correlation and group time delay of ambient noise and ship radiated-noise in the sea","volume":"6","author":"Renhe","year":"1995","journal-title":"Chin. J. Acoust."},{"key":"ref_15","first-page":"125","article-title":"Direction of arrival estimation and signal recovery based on single snapshot compressed sensing in frequency domain","volume":"35","author":"Chunyu","year":"2016","journal-title":"Chin. J. Acoust."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1109\/TAES.2008.4655353","article-title":"Target detection and parameter estimation for MIMO radar systems","volume":"44","author":"Xu","year":"2008","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_17","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_18","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_19","doi-asserted-by":"crossref","first-page":"2669","DOI":"10.1109\/TSP.2011.2125960","article-title":"Transmit energy focusing for DOA estimation in MIMO radar with colocated antennas","volume":"59","author":"Hassanien","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1609","DOI":"10.1109\/LSP.2015.2417220","article-title":"Transmit radiation pattern invariance in MIMO radar with application to DOA estimation","volume":"22","author":"Hassanien","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1490","DOI":"10.1109\/TSP.2014.2299513","article-title":"Efficient transmit beamspace design for search-free based DOA estimation in MIMO radar","volume":"62","author":"Khabbazibasmenj","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"6292","DOI":"10.1109\/TSP.2017.2726993","article-title":"Joint Transmitter-Receiver Optimization in Multitarget MIMO Radar","volume":"65","author":"Luo","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1109\/78.80829","article-title":"A resolution measure for the MUSIC algorithm and its application to plane wave arrivals contaminated by coherent interference","volume":"39","author":"Zhou","year":"1991","journal-title":"Signal Process. IEEE Trans."},{"key":"ref_24","first-page":"141","article-title":"Perturbation characteristics of ambient sea noise caused by submerged objects","volume":"2","author":"Jianheng","year":"2010","journal-title":"Chin. J. Acoust."},{"key":"ref_25","first-page":"227","article-title":"Robust algorithm of direction of arrival estimation for coherent wideband sources in unknown correlated noise fields","volume":"26","author":"Pengxiao","year":"2007","journal-title":"Chin. J. Acoust."},{"key":"ref_26","first-page":"184","article-title":"Fast direction of arrival estimation of wideband sources in unknown correlated noise fields","volume":"25","author":"Zhengjian","year":"2006","journal-title":"Chin. J. Acoust."},{"key":"ref_27","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_28","doi-asserted-by":"crossref","first-page":"8972","DOI":"10.1109\/JSEN.2016.2618770","article-title":"Noise Reduction Method for Acoustic Sensor Arrays in Underwater Noise","volume":"16","author":"Xia","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"5139","DOI":"10.1088\/0266-5611\/19\/6\/058","article-title":"Theory and Applications of Time Reversal and Interferometric Imaging","volume":"19","author":"Borcea","year":"2003","journal-title":"Inverse Probl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1600","DOI":"10.1109\/TAP.2005.846723","article-title":"Time reversal imaging of obscured targets from multistatic data","volume":"53","author":"Devaney","year":"2005","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2650","DOI":"10.1109\/TSP.2015.2417507","article-title":"Performance Analysis of Time-Reversal MUSIC","volume":"63","author":"Ciuonzo","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1024","DOI":"10.1109\/LSP.2017.2704612","article-title":"On Time-Reversal Imaging by Statistical Testing","volume":"24","author":"Ciuonzo","year":"2017","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1109\/LSP.2017.2661246","article-title":"Noncolocated Time-Reversal MUSIC: High-SNR Distribution of Null Spectrum","volume":"24","author":"Ciuonzo","year":"2017","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Cheng, X., and Wang, Y. (2018, January 28\u201331). A Reduced-Complex Method Based on Toeplitz Reconstruction for Direction of Arrival Estimation in Multiple-Input Multiple-Output Sonar. Proceedings of the 2018 OCEANS\u2014MTS\/IEEE Kobe Techno-Oceans (OTO), Kobe, Japan.","DOI":"10.1109\/OCEANSKOBE.2018.8559047"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1049\/el.2010.3279","article-title":"Low-complexity ESPRIT-based DOA estimation for colocated MIMO radar using reduced-dimension transformation","volume":"47","author":"Zhang","year":"2011","journal-title":"Electron. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1049\/el.2016.3818","article-title":"Computationally efficient DOA estimation for monostatic MIMO radar based on covariance matrix reconstruction","volume":"53","author":"Zhang","year":"2017","journal-title":"Electron. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1049\/el.2016.3964","article-title":"Low complexity MUSIC-based direction-of-arrival algorithm for monostatic MIMO radar","volume":"53","author":"Tan","year":"2017","journal-title":"Electron. Lett."},{"key":"ref_38","first-page":"785","article-title":"Real-part elimination of covariance matrix method for direction-of-arrival estimation","volume":"41","author":"Huijun","year":"2016","journal-title":"Acta Acust."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1109\/JOE.2004.836993","article-title":"An ambient noise model for the northeast Pacific Ocean basin","volume":"30","author":"Wagstaff","year":"2005","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1109\/LSP.2015.2504386","article-title":"Joint robust transmit\/receive adaptive beamforming for MIMO radar using probability-constrained optimization","volume":"23","author":"Zhang","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1109\/TAP.1986.1143830","article-title":"Multiple emitter location and signal parameter estimation","volume":"34","author":"Schmidt","year":"1986","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1310","DOI":"10.1109\/78.928686","article-title":"Maximum-likelihood direction-of-arrival estimation in the presence of unknown nonuniform noise","volume":"49","author":"Pesavento","year":"2001","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1783","DOI":"10.1109\/29.60109","article-title":"Performance study of conditional and unconditional direction-of-arrival estimation","volume":"38","author":"Stoica","year":"1990","journal-title":"IEEE Trans. Acoust. Speechand Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/6\/1325\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:38:24Z","timestamp":1760186304000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/6\/1325"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,16]]},"references-count":43,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["s19061325"],"URL":"https:\/\/doi.org\/10.3390\/s19061325","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,16]]}}}