{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,21]],"date-time":"2025-12-21T06:26:30Z","timestamp":1766298390424,"version":"build-2065373602"},"reference-count":64,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T00:00:00Z","timestamp":1720569600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key R&amp;D Program of China","doi-asserted-by":"publisher","award":["2021YFA1000400"],"award-info":[{"award-number":["2021YFA1000400"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The traditional sparse recovery (SR) space-time adaptive processing (STAP) algorithms are greatly affected by grid mismatch, leading to poor performance in airborne bistatic radar clutter suppression. In order to address this issue, this paper proposes an SR STAP algorithm for airborne bistatic radars based on atomic selection under the Bayesian framework. This method adopts the idea of atomic selection for the process of Bayesian inference, continuously evaluating the contribution of atoms to the likelihood function to add or remove atoms, and then using the selected atoms to estimate the clutter support subspace and perform sparse recovery in the clutter support subspace. Due to the inherent sparsity of clutter signals, performing sparse recovery in the clutter support subspace avoids using a massive number of atoms from an overcomplete space-time dictionary, thereby greatly improving computational efficiency. In airborne bistatic radar scenarios where significant grid mismatch exists, this method can mitigate the performance degradation caused by grid mismatch by encrypting grid points. Since the sparse recovery is performed in the clutter support subspace, encrypting grid points does not lead to excessive computational burden. Additionally, this method integrates out the noise term under a new hierarchical Bayesian model, preventing the adverse effects caused by inaccurate noise power estimation during iterations in the traditional SR STAP algorithms, further enhancing its performance. Our simulation results demonstrate the high efficiency and superior clutter suppression performance and target detection performance of this method.<\/jats:p>","DOI":"10.3390\/rs16142534","type":"journal-article","created":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T15:22:05Z","timestamp":1720624925000},"page":"2534","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Efficient Sparse Recovery STAP Algorithm for Airborne Bistatic Radars Based on Atomic Selection under the Bayesian Framework"],"prefix":"10.3390","volume":"16","author":[{"given":"Kun","family":"Liu","sequence":"first","affiliation":[{"name":"National Key Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tong","family":"Wang","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weijun","family":"Huang","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1109\/7.845248","article-title":"Comparison between monostatic and bistatic antenna configurations for STAP","volume":"36","author":"Klemm","year":"2000","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_2","unstructured":"Himed, B., James, H.M., and Zhang, Y.H. (2001, January 3). Bistatic STAP performance analysis in radar applications. Proceedings of the 2001 IEEE Radar Conference, Atlanta, GA, USA."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"932","DOI":"10.1109\/TAES.2017.2768918","article-title":"Clutter suppression and high-resolution imaging of noncooperative ground targets for bistatic airborne radar","volume":"54","author":"Gelli","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_4","unstructured":"Klemm, R. (2000, January 23\u201325). Effect of bistatic radar configurations on STAP. Proceedings of the European Synthetic Aperture Radar Conference, Munich, Germany."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Duan, R., Wang, X., and Chen, Z. (2008, January 2\u20135). Space-time clutter model for airborne bistatic radar with non-Gaussian statistics. Proceedings of the 2008 IEEE Radar Conference, Adelaide, SA, Australia.","DOI":"10.1109\/RADAR.2008.4720814"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1109\/TAES.1974.307893","article-title":"Rapid convergence rate in adaptive arrays","volume":"10","author":"Reed","year":"1974","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_7","unstructured":"Klemm, R. (2002). Principles of Space-Time Adaptive Processing, The Institution of Electrical Engineers."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1109\/TAES.1973.309792","article-title":"Theory of adaptive radar","volume":"9","author":"Brennan","year":"1973","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1109\/7.845251","article-title":"Space-time adaptive radar performance in heterogeneous clutter","volume":"36","author":"Melvin","year":"2000","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_10","first-page":"425","article-title":"Extended factored space\u2013time processing for airborne radar systems","volume":"1","author":"DiPietro","year":"1992","journal-title":"Signals Syst. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"9697","DOI":"10.1109\/TAES.2023.3255840","article-title":"Space-time adaptive processing using deep neural network-based shrinkage algorithm under small training samples","volume":"59","author":"Song","year":"2023","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1149","DOI":"10.1109\/TAES.2021.3122520","article-title":"A parametric approach to space-time adaptive processing in bistatic radar systems","volume":"58","author":"Klintberg","year":"2021","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Song, D., Feng, Q., Chen, S., Xi, F., and Liu, Z. (2022). Random matrix theory-based reduced-dimension space-time adaptive processing under finite training samples. Remote Sens., 14.","DOI":"10.3390\/rs14163959"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2345","DOI":"10.1109\/TSP.2014.2309556","article-title":"Adaptive double subspace signal detection in Gaussian background-Part I: Homogeneous environments","volume":"62","author":"Liu","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"107268","DOI":"10.1016\/j.sigpro.2019.107268","article-title":"Multichannel signal detection in interference and noise when signal mismatch happens","volume":"166","author":"Liu","year":"2020","journal-title":"Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3918","DOI":"10.1109\/TSP.2018.2841860","article-title":"Distributed target detection in partially homogeneous environment when signal mismatch occurs","volume":"66","author":"Liu","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Meng, Z., and Shen, F. (2023). Robust space-time adaptive processing method for GNSS receivers in coherent signal environments. Remote Sens., 15.","DOI":"10.3390\/rs15174212"},{"key":"ref_18","first-page":"1","article-title":"A novel dimension-reduced space-time adaptive processing algorithm for spaceborne multichannel surveillance radar systems based on spatial\u2013temporal 2-D sliding window","volume":"60","author":"Huang","year":"2022","journal-title":"IEEE Geosci. Remote Sens."},{"key":"ref_19","unstructured":"Ward, J., and Steinhardt, A.O. (1994, January 26\u201329). Multiwindow post-Doppler space-time adaptive processing. Proceedings of the IEEE Signal Processing Workshop Statistical Signal Array Processing, Quebec, QC, Canada."},{"key":"ref_20","unstructured":"Ward, J. (1994). Space-Time Adaptive Processing for Airborne Radar, MIT Lincoln Laboratory."},{"key":"ref_21","unstructured":"Borsari, G.K. (1998, January 14). Mitigating effects on STAP processing caused by an inclined array. Proceedings of the 1998 IEEE Radar Conference, Dallas, TX, USA."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Zhao, H., Shi, Y., Zhang, B., and Shi, M. (2014, January 5\u20138). Analysis and simulation of interference suppression for space-time adaptive processing. Proceedings of the IEEE International Conference on Signal Processing, Communications and Computing, Guilin, China.","DOI":"10.1109\/ICSPCC.2014.6986291"},{"key":"ref_23","unstructured":"Himed, B., Zhang, Y., and Hajjari, A. (2002, January 25). STAP with angle-Doppler compensation for bistatic airborne radars. Proceedings of the 2002 IEEE Radar Conference, Long Beach, CA, USA."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1109\/TAES.2007.4285360","article-title":"Adaptive cancellation method for geometry-induced nonstationary bistatic clutter environments","volume":"43","author":"Melvin","year":"2007","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"13121","DOI":"10.3390\/s150613121","article-title":"An efficient adaptive angle-Doppler compensation approach for non-sidelooking airborne radar STAP","volume":"15","author":"Shen","year":"2015","journal-title":"Sensors"},{"key":"ref_26","unstructured":"Lapierre, F.D., Verly, J.G., and Van Droogenbroeck, M. (2003, January 8). New solutions to the problem of range dependence in bistatic STAP radars. Proceedings of the 2003 IEEE Radar Conference, Huntsville, AL, USA."},{"key":"ref_27","unstructured":"Varadarajan, V., and Krolik, J.L. (2003, January 6\u201310). Space-time interpolation for adaptive arrays with limited training data. Proceedings of the 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, Hong Kong, China."},{"key":"ref_28","unstructured":"Varadarajan, V., and Krolik, J.L. (2003, January 9\u201312). Joint space-time interpolation for bistatic STAP. Proceedings of the Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, Pacific Grove, CA, USA."},{"key":"ref_29","unstructured":"Zatman, M. (2001, January 13\u201314). Performance analysis of the derivative based updating method. Proceedings of the Adaptive Sensor Array Processing Workshop, MIT Lincoln Lab., Lexington, MA, USA."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1109\/MSP.2007.4286571","article-title":"Compressive sensing","volume":"24","author":"Baraniuk","year":"2007","journal-title":"IEEE Signal Proc. Mag."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4347","DOI":"10.1109\/TSP.2009.2025979","article-title":"Relaxed conditions for sparse signal recovery with general concave priors","volume":"57","author":"Trzasko","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3397","DOI":"10.1109\/78.258082","article-title":"Matching pursuits with time-frequency dictionaries","volume":"41","author":"Mallat","year":"1993","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4655","DOI":"10.1109\/TIT.2007.909108","article-title":"Signal recovery from random measurements via orthogonal matching pursuit","volume":"53","author":"Tropp","year":"2007","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_34","first-page":"606","article-title":"An interior-point method for large-scale \u21131-regularized logistic regression","volume":"1","author":"Koh","year":"2007","journal-title":"J. Mach. Learn. Res."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/78.558475","article-title":"Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm","volume":"45","author":"Gorodnitsky","year":"1997","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1109\/TAES.2010.5417172","article-title":"Source localization and sensing: A nonparametric iterative adaptive approach based on weighted least squares","volume":"46","author":"Yardibi","year":"2010","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1214","DOI":"10.1109\/LGRS.2012.2236639","article-title":"On clutter sparsity analysis in space-time adaptive processing airborne radar","volume":"10","author":"Yang","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Zhang, S., Wang, T., Liu, C., and Ren, B. (2024). A fast IAA\u2212based SR\u2212STAP method for airborne radar. Remote Sens., 16.","DOI":"10.3390\/rs16081388"},{"key":"ref_39","first-page":"1","article-title":"Gridless sparse clutter nulling STAP based on particle swarm optimization","volume":"19","author":"Li","year":"2022","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"\u015alesicka, A., and Kawalec, A. (2020). An application of the orthogonal matching pursuit algorithm in space-time adaptive processing. Sensors, 20.","DOI":"10.3390\/s20123468"},{"key":"ref_41","unstructured":"Yang, X., Sun, Y., Zeng, T., and Long, T. (2015, January 14\u201316). Iterative roubust sparse recoery method based on focuss for space-time adaptive processing. Proceedings of the IET International Radar Conference, Hangzhou, China."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"3567","DOI":"10.1016\/j.sigpro.2013.03.033","article-title":"Adaptive clutter suppression based on iterative adaptive approach for airborne radar","volume":"93","author":"Yang","year":"2013","journal-title":"Signal Process."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.sigpro.2018.02.008","article-title":"Airborne radar space time adaptive processing based on atomic norm minimization","volume":"148","author":"Feng","year":"2018","journal-title":"Signal Process."},{"key":"ref_44","unstructured":"Grant, M., and Boyd, S. (2024, April 10). CVX: Matlab Software for Disciplined Convex Programing, Version 2.0 Beta. Available online: http:\/\/cvxr.com\/cvx."},{"key":"ref_45","first-page":"211","article-title":"Sparse Bayesian learning and the relevance vector machine","volume":"1","author":"Tipping","year":"2001","journal-title":"J. Mach. Learn."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2346","DOI":"10.1109\/TSP.2007.914345","article-title":"Bayesian compressive sensing","volume":"56","author":"Ji","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2153","DOI":"10.1109\/TSP.2004.831016","article-title":"Sparse Bayesian learning for basis selection","volume":"52","author":"Wipf","year":"2004","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"3704","DOI":"10.1109\/TSP.2007.894265","article-title":"An empirical Bayesian strategy for solving the simultaneous sparse approximation problem","volume":"55","author":"Wipf","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1049\/iet-spr.2016.0183","article-title":"Sparsity-based STAP algorithm with multiple measurement vectors via sparse Bayesian learning strategy for airborne radar","volume":"11","author":"Duan","year":"2017","journal-title":"IET Signal Process."},{"key":"ref_50","first-page":"907","article-title":"Tensor-based sparse recovery space-time adaptive processing for large size data clutter suppression in airborne radar","volume":"59","author":"Cui","year":"2022","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_51","first-page":"907","article-title":"Clutter suppression based on iterative reweighted methods with multiple measurement vectors for airborne radar","volume":"59","author":"Liu","year":"2022","journal-title":"IET Radar Sonar Navig."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Liu, K., Wang, T., Wu, J., Liu, C., and Cui, W. (2022). On the efficient implementation of sparse Bayesian learning-based STAP algorithms. Remote Sens., 14.","DOI":"10.3390\/rs14163931"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"10900","DOI":"10.1109\/JSEN.2023.3263919","article-title":"A clutter suppression algorithm via enhanced sparse bayesian learning for airborne radar","volume":"23","author":"Wang","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Cao, J., Wang, T., and Wang, D. (2024). Beam-space post-Doppler reduced-dimension STAP based on sparse Bayesian learning. Remote Sens., 16.","DOI":"10.3390\/rs16020307"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1380","DOI":"10.1049\/rsn2.12427","article-title":"A novel sparse recovery-based space-time adaptive processing algorithm based on gridless sparse Bayesian learning for non-sidelooking airborne radar","volume":"17","author":"Cui","year":"2023","journal-title":"IET Radar Sonar Navig."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1109\/LSP.2024.3399631","article-title":"On efficient maximum likelihood algorithm for clutter suppression","volume":"31","author":"Zhang","year":"2024","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_57","first-page":"481","article-title":"Empirical Bayes density regression","volume":"17","author":"Dunson","year":"2007","journal-title":"Stat. Sin."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1109\/TSP.2008.2005866","article-title":"Multitask compressive sensing","volume":"57","author":"Ji","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Wu, Q., Zhang, Y.D., Amin, M.G., and Himed, B. (2014, January 4\u20139). Complex multitask Bayesian compressive sensing. Proceedings of the 2014 IEEE International Conference on Acoustics, Speech and Signal Processing, Florence, Italy.","DOI":"10.1109\/ICASSP.2014.6854226"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Golub, G.H., and Van Loan, C.F. (2013). Matrix Computations, Johns Hopkins Univ. Press.","DOI":"10.56021\/9781421407944"},{"key":"ref_61","unstructured":"Wipf, D.P., and Nagarajan, S.S. (2008, January 25\u201328). A New View of Automatic Relevance Determination. Proceedings of the International Conference on Neural Information Processing Systems, Auckland, New Zealand."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.sigpro.2016.06.023","article-title":"Clutter suppression algorithm based on fast converging sparse Bayesian learning for airborne radar","volume":"130","author":"Wang","year":"2017","journal-title":"Signal Process."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1109\/7.135446","article-title":"A CFAR adaptive matched filter detector","volume":"28","author":"Robey","year":"1992","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"121301","DOI":"10.1007\/s11432-020-3211-8","article-title":"Multichannel adaptive signal detection: Basic theory and literature review","volume":"65","author":"Liu","year":"2022","journal-title":"Sci. China Inf. Sci."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/14\/2534\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:12:52Z","timestamp":1760109172000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/14\/2534"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,10]]},"references-count":64,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2024,7]]}},"alternative-id":["rs16142534"],"URL":"https:\/\/doi.org\/10.3390\/rs16142534","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2024,7,10]]}}}