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Foundation","award":["YYJC022022018"],"award-info":[{"award-number":["YYJC022022018"]}]},{"name":"China Postdoctoral Science Foundation","award":["2020M681585"],"award-info":[{"award-number":["2020M681585"]}]},{"name":"China Postdoctoral Science Foundation","award":["2023T160312"],"award-info":[{"award-number":["2023T160312"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Due to their ability to achieve higher DOA estimation accuracy and larger degrees of freedom (DOF) using a fixed number of antennas, sparse arrays, etc., nested and coprime arrays have attracted a lot of attention in relation to research into direction of arrival (DOA) estimation. However, the usage of the sparse array is based on the assumption that the signals are independent of each other, which is hard to guarantee in practice due to the complex propagation environment. To address the challenge of sparse arrays struggling to handle coherent wideband signals, we propose the following method. Firstly, we exploit the coherent signal subspace method (CSSM) to focus the wideband signals on the reference frequency and assist in the decorrelation process, which can be implemented without any pre-estimations. Then, we virtualize the covariance matrix of sparse array due to the decorrelation operation. Next, an enhanced spatial smoothing algorithm is applied to make full use of the information available in the data covariance matrix, as well as to improve the decorrelation effect, after which stage the multiple signal classification (MUSIC) algorithm is used to obtain DOA estimations. In the simulation, with reference to the root mean square error (RMSE) that varies in tandem with the signal-to-noise ratio (SNR), the algorithm achieves satisfactory results compared to other state-of-the-art algorithms, including sparse arrays using the traditional incoherent signal subspace method (ISSM), the coherent signal subspace method (CSSM), spatial smoothing algorithms, etc. Furthermore, the proposed method is also validated via real data tests, and the error value is only 0.2 degrees in real data tests, which is lower than those of the other methods in real data tests.<\/jats:p>","DOI":"10.3390\/s23156984","type":"journal-article","created":{"date-parts":[[2023,8,6]],"date-time":"2023-08-06T10:01:53Z","timestamp":1691316113000},"page":"6984","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Direction of Arrival Estimation of Coherent Wideband Sources Using Nested Array"],"prefix":"10.3390","volume":"23","author":[{"given":"Yawei","family":"Tang","sequence":"first","affiliation":[{"name":"College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weiming","family":"Deng","sequence":"additional","affiliation":[{"name":"College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianfeng","family":"Li","sequence":"additional","affiliation":[{"name":"College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaofei","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,6]]},"reference":[{"key":"ref_1","unstructured":"Tuncer, T.E., and Friedlander, B. (2009). Classical and Modern Direction-of-Arrival Estimation, Academic Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1109\/LCOMM.2020.3032733","article-title":"Angle Separation Learning for Coherent DOA Estimation with Deep Sparse Prior","volume":"25","author":"Xiang","year":"2021","journal-title":"IEEE Commun. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Jiang, H., Li, L., Zhang, H., Pan, H., and Li, X. (2022, January 16\u201318). Stepwise DOA Estimation for Coherent and Uncorrelated Mixed Signals on Coprime Array. Proceedings of the 2022 IEEE 5th Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC), Chongqing, China.","DOI":"10.1109\/IMCEC55388.2022.10020000"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Li, J.F., Li, P., Li, P., Tang, L.M., Zhang, X.F., and Wu, Q.H. (2022). Self-Position Awareness Based on Cascade Direct Localization Over Multiple Source Data. IEEE Trans. Intell. Transp. Syst., 9.","DOI":"10.1109\/TITS.2022.3170465"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2475","DOI":"10.1109\/TSP.2017.2666779","article-title":"Direct Localization for Massive MIMO","volume":"65","author":"Garcia","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_6","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_7","doi-asserted-by":"crossref","unstructured":"Choi, S., Kim, B., Kim, J., Kim, D., and Cho, H. (2019, January 15\u201316). Doppler Coherent Focusing DOA Method for Efficient Radar Map Generation. Proceedings of the 5th IEEE MTT-S International Conference on Microwaves for Intelligent Mobility (ICMIM), Detroit, MI, USA.","DOI":"10.1109\/ICMIM.2019.8726675"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Millhiser, J., Sarangi, P., and Pal, P. (2022, January 22\u201327). Initialization-Free Implicit-Focusing (IF2) for Wideband Direction-of-Arrival Estimation. Proceedings of the 47th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Singapore.","DOI":"10.1109\/ICASSP43922.2022.9746772"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1657","DOI":"10.1109\/TSP.2022.3160802","article-title":"DOA Estimation for Heterogeneous Wideband Sources Based on Adaptive Space-Frequency Joint Processing","volume":"70","author":"Zhang","year":"2022","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1977","DOI":"10.1109\/TSP.2006.872581","article-title":"TOPS: New DOA estimator for wideband signals","volume":"54","author":"Yoon","year":"2006","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","unstructured":"Yuanyuan, J., Dan, L., Xiaohuan, W., and Wei-Ping, Z. (2020, January 8\u201311). A Gridless Wideband DOA Estimation Based On Atomic Norm Minimization. Proceedings of the 2020 IEEE 11th Sensor Array and Multichannel Signal Processing Workshop (SAM), Hangzhou, China."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Kulhandjian, H., Kulhandjian, M., Kim, Y., and D\u2019Amours, C. (2018, January 20\u201324). 2-D DOA Estimation of Coherent Wideband Signals with Auxiliary-Vector Basis. Proceedings of the IEEE International Conference on Communications (ICC), Kansas City, MO, USA.","DOI":"10.1109\/ICCW.2018.8403682"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2502","DOI":"10.1109\/78.224260","article-title":"Beamspace Root-Music for Minimum Redundancy Linear Arrays","volume":"41","author":"Zoltowski","year":"1993","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"752","DOI":"10.1109\/LCOMM.2018.2802491","article-title":"Extended-Aperture Unitary Root MUSIC-Based DOA Estimation for Coprime Array","volume":"22","author":"Li","year":"2018","journal-title":"IEEE Commun. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1109\/LSP.2021.3139577","article-title":"Coprime Nested Arrays for DOA Estimation: Exploiting the Nesting Property of Coprime Array","volume":"29","author":"Peng","year":"2022","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Qin, Y.H., Liu, Y.M., Liu, J.Y., and Yu, Z.Y. (2018). Underdetermined Wideband DOA Estimation for Off-Grid Sources with Coprime Array Using Sparse Bayesian Learning. Sensors, 18.","DOI":"10.3390\/s18010253"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1208","DOI":"10.1109\/LCOMM.2018.2821672","article-title":"Generalized Nested Array: Optimization for Degrees of Freedom and Mutual Coupling","volume":"22","author":"Shi","year":"2018","journal-title":"IEEE Commun. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1109\/LSP.2020.2983611","article-title":"Extended Nested Arrays for Consecutive Virtual Aperture Enhancement","volume":"27","author":"Ren","year":"2020","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1109\/TASSP.1985.1164649","article-title":"On spatial smoothing for direction-of-arrival estimation of coherent signals","volume":"ASSP-33","author":"Shan","year":"1985","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.1109\/29.7543","article-title":"Maximum likelihood localization of multiple sources by alternating projection","volume":"36","author":"Ziskind","year":"1988","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1109\/TAP.1986.1143956","article-title":"A vector space approach to direction finding in a coherent multipath environment","volume":"AP-34","author":"Zoltowski","year":"1986","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1109\/29.17496","article-title":"Forward\/backward spatial smoothing techniques for coherent signal identification","volume":"37","author":"Pillai","year":"1989","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1109\/TSP.2015.2480044","article-title":"Performance Analysis of Spatial Smoothing Schemes in the Context of Large Arrays","volume":"64","author":"Pham","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.1109\/LGRS.2013.2292825","article-title":"Time-Delay Estimation for Ground Penetrating Radar Using ESPRIT With Improved Spatial Smoothing Technique","volume":"11","author":"Qu","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Jin, A.S., and Zhang, F. (2020, January 6\u20138). 2D DOA estimation of coherent sources based on reconstruction of Toeplitz matrix sets. Proceedings of the Chinese Automation Congress (CAC), Shanghai, China.","DOI":"10.1109\/CAC51589.2020.9327264"},{"key":"ref_26","unstructured":"Liu, X.Z., Song, M.Y., and Yang, Y.H. (2017, January 28\u201330). An Effective DOA Estimation Method of Coherent Signals Based on Reconstruct Weighted Noise Subspace. Proceedings of the 29th Chinese Control And Decision Conference (CCDC), Chongqing, China."},{"key":"ref_27","unstructured":"Evans, J.E., Sun, D.F., and Johnson, J.R. (1982). Application of Advanced Signal Processing Techniques to Angle of Arrival Estimation in ATC Navigation and Surveillance Systems, Massachusetts Institute of Technology, Lincoln Laboratory."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1109\/TASSP.1984.1164400","article-title":"Spatio-temporal spectral analysis by eigenstructure methods","volume":"ASSP-32","author":"Wax","year":"1984","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Shi, J., Zhang, Q.F., and Wang, Y. (2017, January 22\u201325). Wideband DOA Estimation based on A-Shaped Array. Proceedings of the IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC), Xiamen, China.","DOI":"10.1109\/ICSPCC.2017.8242605"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Yadav, A.K., and Santosh, S. (2016, January 20\u201321). Comparative Analysis of Wideband DOA Estimation Methods with Nested Array. Proceedings of the 2016 IEEE International Conference on Recent Trends in Electronics, Information & Communication Technology (RTEICT), Bengaluru, India.","DOI":"10.1109\/RTEICT.2016.7808054"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1109\/TAP.1986.1143830","article-title":"Multiple emitter location and signal parameter estimation","volume":"AP-34","author":"Schmidt","year":"1986","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2179","DOI":"10.1109\/78.950774","article-title":"WAVES: Weighted average of signal subspaces for robust wideband direction finding","volume":"49","author":"Parisi","year":"2001","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Pal, P., and Vaidyanathan, P.P. (2009, January 1\u20134). A Novel Autofocusing Approach for Estimating Directions-of-Arrival of Wideband Signals. Proceedings of the 2009 43rd Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA.","DOI":"10.1109\/ACSSC.2009.5469796"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1109\/TASSP.1985.1164667","article-title":"Coherent signal-subspace processing for the detection and estimation of angles of arrival of multiple wide-band sources","volume":"ASSP-33","author":"Wang","year":"1985","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Bo, L.K., Xiong, J.Y., and Luo, L.Y. (2013, January 12\u201313). A Novel Wideband DOA Estimation Method Using Direction-Free Focusing Matrix. Proceedings of the 3rd International Conference on Computer Science and Network Technology (ICCSNT), Dalian, China.","DOI":"10.1109\/ICCSNT.2013.6967287"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.1109\/29.1655","article-title":"Focussing matrices for coherent signal-subspace processing","volume":"36","author":"Hung","year":"1988","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"752","DOI":"10.1109\/78.489056","article-title":"The optimal focusing subspace for coherent signal subspace processing","volume":"44","author":"Valaee","year":"1996","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/15\/6984\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:26:48Z","timestamp":1760128008000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/15\/6984"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,6]]},"references-count":37,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["s23156984"],"URL":"https:\/\/doi.org\/10.3390\/s23156984","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,6]]}}}