{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:12:57Z","timestamp":1760242377183,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2017,6,9]],"date-time":"2017-06-09T00:00:00Z","timestamp":1496966400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Generally, many beamforming methods are derived under the assumption of white noise. In practice, the actual underwater ambient noise is complex. As a result, the noise removal capacity of the beamforming method may be deteriorated considerably. Furthermore, in underwater environment with extremely low signal-to-noise ratio (SNR), the performances of the beamforming method may be deteriorated. To tackle these problems, a noise removal method for uniform circular array (UCA) is proposed to remove the received noise and improve the SNR in complex noise environments with low SNR. First, the symmetrical noise sources are defined and the spatial correlation of the symmetrical noise sources is calculated. Then, based on the preceding results, the noise covariance matrix is decomposed into symmetrical and asymmetrical components. Analysis indicates that the symmetrical component only affect the real part of the noise covariance matrix. Consequently, the delay-and-sum (DAS) beamforming is performed by using the imaginary part of the covariance matrix to remove the symmetrical component. However, the noise removal method causes two problems. First, the proposed method produces a false target. Second, the proposed method would seriously suppress the signal when it is located in some directions. To solve the first problem, two methods to reconstruct the signal covariance matrix are presented: based on the estimation of signal variance and based on the constrained optimization algorithm. To solve the second problem, we can design the array configuration and select the suitable working frequency. Theoretical analysis and experimental results are included to demonstrate that the proposed methods are particularly effective in complex noise environments with low SNR. The proposed method can be extended to any array.<\/jats:p>","DOI":"10.3390\/s17061345","type":"journal-article","created":{"date-parts":[[2017,6,9]],"date-time":"2017-06-09T10:29:59Z","timestamp":1497004199000},"page":"1345","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Noise Removal Method for Uniform Circular Arrays in Complex Underwater Noise Environments with Low SNR"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5792-4130","authenticated-orcid":false,"given":"Huijun","family":"Xia","sequence":"first","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"},{"name":"Key Laboratory of Ocean Acoustics and Sensing, Ministry of Industry and Information Technology, Xi\u2019an 710072, China"}]},{"given":"Kunde","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"},{"name":"Key Laboratory of Ocean Acoustics and Sensing, Ministry of Industry and Information Technology, Xi\u2019an 710072, China"}]},{"given":"Yuanliang","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"},{"name":"Key Laboratory of Ocean Acoustics and Sensing, Ministry of Industry and Information Technology, Xi\u2019an 710072, China"}]},{"given":"Yong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710072, China"}]},{"given":"Yaxiong","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710072, China"},{"name":"Key Laboratory of Ocean Acoustics and Sensing, Ministry of Industry and Information Technology, Xi\u2019an 710072, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,6,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2230","DOI":"10.1109\/TSP.2002.801937","article-title":"GSVD-based optimal filtering for single and multimicrophone speech enhancement","volume":"50","author":"Doclo","year":"2002","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3718","DOI":"10.1109\/TSP.2005.855110","article-title":"Prewhitening for rank-deficient noise in subspace methods for noise reduction","volume":"53","author":"Hansen","year":"2005","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"12424","DOI":"10.3390\/s120912424","article-title":"A Nonlinear Adaptive Beamforming Algorithm Based on Least Squares Sipport Vector Regression","volume":"12","author":"Lutao","year":"2012","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1408","DOI":"10.1109\/PROC.1969.7278","article-title":"High resolution frequency-wavenumber spectrum analysis","volume":"57","author":"Capon","year":"1969","journal-title":"Proc. IEEE"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1702","DOI":"10.1109\/TSP.2003.812831","article-title":"On robust Capon beamforming and diagonal loading","volume":"51","author":"Li","year":"2003","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1109\/TSP.2005.861052","article-title":"Finite sample size effect on minimum variance beamformers: Optimum diagonal loading factor for large arrays","volume":"54","author":"Mestre","year":"2006","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1109\/TAES.2010.5417174","article-title":"Fully automatic computation of diagonal loading levels for robust adaptive beamforming","volume":"46","author":"Du","year":"2010","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1010","DOI":"10.1121\/1.1912921","article-title":"Review of Underwater Acoustics Research: Noise","volume":"51","author":"Gordon","year":"1972","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1732","DOI":"10.1121\/1.1909110","article-title":"Spatial-Correlation Functions for Various Noise Models","volume":"34","author":"Cron","year":"1962","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1936","DOI":"10.1121\/1.1909155","article-title":"Acoustic Ambient Noise in the Ocean: Spectra and Sources","volume":"34","author":"Gordon","year":"1962","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2643","DOI":"10.1121\/1.3688506","article-title":"Cross-correlation in band-limited ocean ambient noise fields","volume":"131","author":"Michael","year":"2012","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1109\/TAES.2008.4655365","article-title":"Maximum likelihood DOA estimation in unknown colored noise fields","volume":"44","author":"Li","year":"2008","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1109\/TSP.2004.838966","article-title":"Maximum likelihood direction-of-arrival estimation in unknown noise fields using sparse sensor arrays","volume":"53","author":"Vorobyov","year":"2005","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3008","DOI":"10.1109\/TSP.2016.2537265","article-title":"Iterative Methods for Subspace and DOA Estimation in Nonuniform Noise","volume":"64","author":"Liao","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","unstructured":"Shen, W.M. (1989). High-Resolution Bearing Estimation for Weak Signals in Nonwhite Noise Field. [Master\u2019s Thesis, Northwestern Polytechnical University]."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Zhang, D., Ma, Y., Yang, K., and Pan, Y. (2008, January 27\u201330). Weak Signal Detection Method Based on Sector Spatial Pre-Filtering. Proceedings of the International Congress on Image and Signal Processing (CISP \u201908), Sanya, China.","DOI":"10.1109\/CISP.2008.225"},{"key":"ref_17","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_18","doi-asserted-by":"crossref","first-page":"144302","DOI":"10.7498\/aps.65.144302","article-title":"Analysis of the symmetry of the ambient noise and study of the noise reduction","volume":"65","author":"Xia","year":"2016","journal-title":"Acta Phys. Sin."},{"key":"ref_19","unstructured":"Farrier, D., and Jeffries, D. (1985, January 26\u201329). Bearing estimation in the presence of unknown correlation noise. Proceedings of the IEEE International Conference on Acoustic, Speech, and Signal Processing, Tampa, FL, USA."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Carey, W., and Evans, R. (2011). Ocean Ambient Noise\u2014Measurement and Theory, Springer.","DOI":"10.1007\/978-1-4419-7832-5"},{"key":"ref_21","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_22","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1121\/1.1909312","article-title":"Vertical directionality of ambient noise in the deep ocean at a site near Bermuda","volume":"37","author":"Axelrod","year":"1965","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_23","first-page":"6","article-title":"Directivity Prediction on Tone Noise of Propeller Operating in Non-Uniform Flows","volume":"5","author":"Xie","year":"2010","journal-title":"Chin. J. Ship Res."},{"key":"ref_24","unstructured":"Robert, J. (1983). Principles of Underwater Sound, McGraw-Hill Book Company."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3464","DOI":"10.1121\/1.2799929","article-title":"Generating Sensor Signals in Isotropic Noise Fields","volume":"122","author":"Sharon","year":"2007","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/0165-1684(88)90027-8","article-title":"Acoustic noise analysis and speech enhancement techniques for mobile radio applications","volume":"15","author":"Neviano","year":"1988","journal-title":"Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1109\/25.61353","article-title":"Speech enhancement for mobile telephony","volume":"39","author":"Goulding","year":"1990","journal-title":"IEEE Trans. Veh. Technol."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/6\/1345\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:38:32Z","timestamp":1760207912000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/6\/1345"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,9]]},"references-count":27,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2017,6]]}},"alternative-id":["s17061345"],"URL":"https:\/\/doi.org\/10.3390\/s17061345","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,6,9]]}}}