{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:09:13Z","timestamp":1760234953688,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2021,6,27]],"date-time":"2021-06-27T00:00:00Z","timestamp":1624752000000},"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>An enhanced smoothed l0-norm algorithm for the passive phased array system, which uses the covariance matrix of the received signal, is proposed in this paper. The SL0 (smoothed l0-norm) algorithm is a fast compressive-sensing-based DOA (direction-of-arrival) estimation algorithm that uses a single snapshot from the received signal. In the conventional SL0 algorithm, there are limitations in the resolution and the DOA estimation performance, since a single sample is used. If multiple snapshots are used, the conventional SL0 algorithm can improve performance in terms of the DOA estimation. In this paper, a covariance-fitting-based SL0 algorithm is proposed to further reduce the number of optimization variables when using multiple snapshots of the received signal. A cost function and a new null-space projection term of the sparse recovery for the proposed scheme are presented. In order to verify the performance of the proposed algorithm, we present the simulation results and the experimental results based on the measured data.<\/jats:p>","DOI":"10.3390\/s21134403","type":"journal-article","created":{"date-parts":[[2021,6,27]],"date-time":"2021-06-27T23:57:22Z","timestamp":1624838242000},"page":"4403","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["An Enhanced Smoothed L0-Norm Direction of Arrival Estimation Method Using Covariance Matrix"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3610-3258","authenticated-orcid":false,"given":"Ji Woong","family":"Paik","sequence":"first","affiliation":[{"name":"Radar System Team 2, Hanwha Systems, Yongin-City 17121, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3715-3943","authenticated-orcid":false,"given":"Joon-Ho","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Information and Communication Engineering, Sejong University, Seoul 05006, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9022-8425","authenticated-orcid":false,"given":"Wooyoung","family":"Hong","sequence":"additional","affiliation":[{"name":"Department of Defense Systems Engineering, Sejong University, Seoul 05006, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/79.526899","article-title":"Two decades of array signal processing research-The parametric approach","volume":"13","author":"Krim","year":"1996","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2020\/7515139","article-title":"Performance analysis of conventional beamforming algorithm for angle-of-arrival estimation under measurement uncertainty","volume":"2020","author":"Lee","year":"2020","journal-title":"Int. J. Antennas Propag."},{"key":"ref_3","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_4","doi-asserted-by":"crossref","first-page":"19","DOI":"10.2528\/PIER12122711","article-title":"Efficient Implementation of the Capon beamforming using the Levenberg\u2013Marquardt scheme for two dimensional AOA estimation","volume":"137","author":"Cho","year":"2013","journal-title":"Prog. Electromagn. Res."},{"key":"ref_5","first-page":"243","article-title":"Multiple emitter location and signal parameter estimation","volume":"34","author":"Schmidt","year":"1979","journal-title":"Proc. Radc Spectr. Est. Work. Shop"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Paik, J.W., Lee, K., and Lee, J. (2020). Asymptotic performance analysis of maximum likelihood algorithm for direction-of-arrival estimation: Explicit expression of estimation error and mean square error. Appl. Sci., 10.","DOI":"10.3390\/app10072415"},{"key":"ref_7","first-page":"1","article-title":"Performance analysis of two-dimensional maximum likelihood direction-of-arrival estimation algorithm using the UCA","volume":"2017","author":"Ho","year":"2017","journal-title":"Int. J. Antennas Propag."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3010","DOI":"10.1109\/TSP.2005.850882","article-title":"A sparse signal reconstruction perspective for source localization with sensor arrays","volume":"53","author":"Malioutov","year":"2005","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Paik, J.W., Hong, W., and Lee, J. (2020). Direction-of-departure and direction-of-arrival estimation algorithm based on compressive sensing: Data-Fitting. Remote Sens., 12.","DOI":"10.3390\/rs12172773"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zheng, J., Kaveh, M., and Tsuji, H. (September, January 31). Sparse spectral fitting for direction of arrival and power estimation. Proceedings of the 2009 IEEE\/SP 15th Workshop on Statistical Signal Processing, Cardiff, UK.","DOI":"10.1109\/SSP.2009.5278548"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2767","DOI":"10.1109\/TSP.2013.2256903","article-title":"Sparse Spatial Spectral Estimation: A Covariance Fitting Algorithm, Performance and Regularization","volume":"61","author":"Zheng","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3883","DOI":"10.1121\/1.5042354","article-title":"Statistics on noise covariance matrix for covariance fitting-based compressive sensing direction-of-arrival estimation algorithm: For use with optimization via regularization","volume":"143","author":"Paik","year":"2018","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1109\/TSP.2008.2007606","article-title":"A fast approach for overcomplete sparse decomposition based on smoothed l0 norm","volume":"57","author":"Mohimani","year":"2009","journal-title":"IEE Trans. Signal Process."},{"key":"ref_14","unstructured":"Oxvig, C.S., Pedersen, P.S., Arildsen, T., and Larsen, T. (2013, March 01). Improving Smoothed l0 Norm in Compressive Sensing using Adaptive Parameter Selection. Available online: https:\/\/arxiv.org\/abs\/1210.4277."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1068","DOI":"10.3390\/s17051068","article-title":"Joint smoothed l0 norm DOA estimation algorithm for multiple measurement vectors in MIMO radar","volume":"17","author":"Zhou","year":"2017","journal-title":"Sensors"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.sigpro.2017.01.034","article-title":"Reweighted smoothed l0 norm based DOA estimation for MIMO radar","volume":"137","author":"Liui","year":"2017","journal-title":"Elsevier Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1170","DOI":"10.1049\/iet-rsn.2016.0538","article-title":"Robust smoothed l0-norm based approach for MIMO radar target estimation","volume":"11","author":"Chen","year":"2017","journal-title":"IET Radar Sonar Navig."},{"key":"ref_18","first-page":"1","article-title":"Adaptive beamforming based on compressed sensing with smoothed l0 norm","volume":"2015","author":"Han","year":"2015","journal-title":"Int. J. Antennas Propag."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1109\/JSEE.2016.00059","article-title":"DOA estimation via sparse recovering from the smoothed covariance vector","volume":"27","author":"Cai","year":"2016","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1049\/ell2.12158","article-title":"Noise radar range doppler imaging via 2D generalized smoothed-l0","volume":"57","author":"Lu","year":"2021","journal-title":"Electron. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Wang, L., Yin, X., Yue, H., and Xiang, J. (2018). A regularized weighted smoothed L0 norm minimization method for underdetermined blind source separation. Sensors, 2018.","DOI":"10.3390\/s18124260"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Yang, Z., An, G., Zhang, R., Ruan, Q., and Li, C. (2020, January 6\u20139). Smoothing Modified Newton Algorithm Based on LpNorm Regularization for Signal Recovery. Proceedings of the 2020 15th IEEE International Conference on Signal Processing (ICSP), Beijing, China.","DOI":"10.1109\/ICSP48669.2020.9321071"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/13\/4403\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:25:16Z","timestamp":1760163916000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/13\/4403"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,27]]},"references-count":22,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["s21134403"],"URL":"https:\/\/doi.org\/10.3390\/s21134403","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2021,6,27]]}}}