{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T13:13:56Z","timestamp":1775913236672,"version":"3.50.1"},"reference-count":53,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T00:00:00Z","timestamp":1660521600000},"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":["6217011933"],"award-info":[{"award-number":["6217011933"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["BK20221486"],"award-info":[{"award-number":["BK20221486"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Jiangsu Province","award":["6217011933"],"award-info":[{"award-number":["6217011933"]}]},{"name":"Natural Science Foundation of Jiangsu Province","award":["BK20221486"],"award-info":[{"award-number":["BK20221486"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Space-time adaptive processing (STAP) is a fundamental topic in airborne radar applications due to its clutter suppression ability. Reduced-dimension (RD)-STAP can release the requirement of the number of training samples and reduce the computational load from traditional STAP, which attracts much attention. However, under the situation that training samples are severely deficient, RD-STAP will become poor like the traditional STAP. To enhance RD-STAP performance in such cases, this paper develops a novel RD-STAP algorithm using random matrix theory (RMT), RMT-RD-STAP. By minimizing the output clutter-plus-noise power, the estimate of the inversion of clutter plus noise covariance matrix (CNCM) can be obtained through optimally manipulating its eigenvalues, thus producing the optimal STAP weight vector. Specifically, the clutter-related eigenvalues are estimated according to the clutter-related sample eigenvalues via RMT, and the noise-related eigenvalue is optimally selected from the noise-related sample eigenvalues. It is found that RMT-RD-STAP significantly outperforms the RD-STAP algorithm when the RMB rule cannot be satisfied. Theoretical analyses and numerical results demonstrate the effectiveness and the performance advantages of the proposed RMT-RD-STAP algorithm.<\/jats:p>","DOI":"10.3390\/rs14163959","type":"journal-article","created":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T23:44:03Z","timestamp":1660607043000},"page":"3959","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Random Matrix Theory-Based Reduced-Dimension Space-Time Adaptive Processing under Finite Training Samples"],"prefix":"10.3390","volume":"14","author":[{"given":"Di","family":"Song","sequence":"first","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"given":"Qi","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"given":"Shengyao","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4170-3023","authenticated-orcid":false,"given":"Feng","family":"Xi","sequence":"additional","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"given":"Zhong","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1109\/TAES.1973.309792","article-title":"Theory of adaptive radar","volume":"AES-9","author":"Brennan","year":"1973","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_2","unstructured":"Ward, J. (1994). Space-Time Adaptive Processing for Airborne Radar, MIT Lincoln Lab.. Technical Report 1015."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1109\/MAES.2004.1263229","article-title":"A STAP overview","volume":"19","author":"Melvin","year":"2004","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1109\/TAES.1974.307893","article-title":"Rapid convergence rate in adaptive arrays","volume":"AES-10","author":"Reed","year":"1974","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Klemm, R. (2006). Principles of Space-Time Adaptive Processing, IET. [3rd ed.].","DOI":"10.1049\/PBRA021E"},{"key":"ref_6","unstructured":"Guerci, J.R. (2003). Space-Time Adaptive Processing for Radar, Artech House."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1214","DOI":"10.1109\/LGRS.2012.2236639","article-title":"On Clutter Sparsity Analysis in Space\u2013Time Adaptive Processing Airborne Radar","volume":"10","author":"Yang","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1510","DOI":"10.1109\/JSTSP.2015.2464187","article-title":"Low-Rank Matrix Decomposition and Spatio-Temporal Sparse Recovery for STAP Radar","volume":"9","author":"Sen","year":"2015","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1109\/TSP.2011.2172435","article-title":"L1-Regularized STAP algorithms with a generalized sidelobe canceler architecture for airborne radar","volume":"60","author":"Yang","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1109\/TAES.2019.2921141","article-title":"Reduced dimension STAP based on sparse recovery in heterogeneous clutter environments","volume":"56","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1109\/MSP.2006.1593336","article-title":"Knowledge-aided adaptive radar at DARPA: An overview","volume":"23","author":"Guerci","year":"2006","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1109\/LSP.2006.888088","article-title":"Knowledge-Aided Bayesian Detection in Heterogeneous Environments","volume":"14","author":"Besson","year":"2007","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1850","DOI":"10.1109\/TAES.2018.2805141","article-title":"Knowledge-Aided Bayesian Space-Time Adaptive Processing","volume":"54","author":"Riedl","year":"2018","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2601","DOI":"10.1109\/TAES.2018.2813898","article-title":"Multimodel Shrinkage for Knowledge-Aided Space-Time Adaptive Processing","volume":"54","author":"Riedl","year":"2018","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1049\/rsn2.12176","article-title":"Deep learning for high-resolution estimation of clutter angle-Doppler spectrum in STAP","volume":"16","author":"Duan","year":"2022","journal-title":"IET Radar Sonar Navig."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Zou, B., Wang, X., Feng, W., Zhu, H., and Lu, F. (2022). DU-CG-STAP Method Based on Sparse Recovery and Unsupervised Learning for Airborne Radar Clutter Suppression. Remote Sens., 14.","DOI":"10.3390\/rs14143472"},{"key":"ref_17","first-page":"1","article-title":"Deep Unfolding Based Space-Time Adaptive Processing Method for Airborne Rada","volume":"11","author":"Zhu","year":"2022","journal-title":"J. Radars"},{"key":"ref_18","unstructured":"DiPietro, R.C. (1992, January 26\u201328). Extended factored space-time processing for airborne radar systems. Proceedings of the Conference Record of the Twenty-Sixth Asilomar Conference on Signals, Systems & Computers, Pacific Grove, CA, USA."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1109\/8.910535","article-title":"A deterministic least-squares approach to space-time adaptive processing (STAP)","volume":"49","author":"Sarkar","year":"2001","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1109\/7.845254","article-title":"STAP for clutter suppression with sum and difference beams","volume":"36","author":"Brown","year":"2000","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1109\/TAES.2013.120145","article-title":"A Method for Finding Best Channels in Beam-Space Post-Doppler Reduced-Dimension STAP","volume":"50","author":"Zhang","year":"2014","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1049\/ip-f-1.1987.0054","article-title":"Adaptive airborne MTI: An auxiliary channel approach","volume":"134","author":"Klemm","year":"1987","journal-title":"IEE Proc. F Commun. Radar Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1109\/7.303737","article-title":"On adaptive spatial-temporal processing for airborne surveillance radar systems","volume":"30","author":"Wang","year":"1994","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_24","first-page":"2757","article-title":"Spectrum estimation for large dimensional covariance matrices using random matrix theory","volume":"36","author":"Karoui","year":"2008","journal-title":"Ann. Statist."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1111\/j.0006-341X.2001.01173.x","article-title":"Shrinkage estimators for covariance matrices","volume":"57","author":"Daniels","year":"2001","journal-title":"Biometrics"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.jeconom.2008.09.017","article-title":"High dimensional covariance matrix estimation using a factor model","volume":"147","author":"Fan","year":"2008","journal-title":"J. Econ."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1933","DOI":"10.1109\/TSP.2018.2799183","article-title":"High-Dimensional MVDR Beamforming: Optimized Solutions Based on Spiked Random Matrix Models","volume":"66","author":"Yang","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Bai, Z., and Silverstein, J.W. (2010). Spectral Analysis of Large Dimensional Random Matrices, Springer.","DOI":"10.1007\/978-1-4419-0661-8"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1006\/jmva.1995.1058","article-title":"Analysis of the Limiting Spectral Distribution of Large Dimensional Random Matrices","volume":"54","author":"Silverstein","year":"1995","journal-title":"J. Multivar. Anal."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1093\/biomet\/84.2.327","article-title":"Asymptotics of eigenprojections of correlation matrices with some applications in principal components analysis","volume":"84","author":"Schott","year":"1997","journal-title":"Biometrika"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1214\/aop\/1022855421","article-title":"No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices","volume":"26","author":"Bai","year":"1998","journal-title":"Ann. Probab."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1006\/jmva.1995.1083","article-title":"Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices","volume":"55","author":"Silverstein","year":"1995","journal-title":"J. Multivar. Anal."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1016\/j.jmva.2015.04.006","article-title":"Spectrum estimation: A unified framework for covariance matrix estimation and PCA in large dimensions","volume":"139","author":"Ledoit","year":"2015","journal-title":"J. Multivar. Anal."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4349","DOI":"10.1093\/rfs\/hhx052","article-title":"Nonlinear shrinkage of the covariance matrix for portfolio selection: Markowitz meets Goldilocks","volume":"30","author":"Ledoit","year":"2017","journal-title":"Rev. Financ. Stud."},{"key":"ref_35","first-page":"37","article-title":"Asymptotic behavior of eigenvalues of empirical covariance matrices","volume":"44","author":"Girko","year":"1992","journal-title":"Theory Probab. Math. Stat."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1109\/JSTSP.2012.2202634","article-title":"Performance Analysis and Optimal Selection of Large Minimum Variance Portfolios Under Estimation Risk","volume":"6","author":"Rubio","year":"2012","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1214\/aoms\/1177704248","article-title":"Asymptotic Theory for Principal Component Analysis","volume":"34","author":"Anderson","year":"1963","journal-title":"Ann. Math. Stat."},{"key":"ref_38","first-page":"97","article-title":"Asymptotic theory for principal component analysis in the complex case","volume":"3","author":"Gupta","year":"1965","journal-title":"J. Indian Statist. Assoc."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1070\/SM1967v001n04ABEH001994","article-title":"Distribution of Eigenvalues for Some Sets of Random Matrices","volume":"1","author":"Marcenko","year":"1967","journal-title":"Math. USSR-Sb."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1643","DOI":"10.1214\/009117905000000233","article-title":"Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices","volume":"33","author":"Baik","year":"2005","journal-title":"Ann. Probab."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1382","DOI":"10.1016\/j.jmva.2005.08.003","article-title":"Eigenvalues of large sample covariance matrices of spiked population models","volume":"97","author":"Baik","year":"2006","journal-title":"J. Multivar. Anal."},{"key":"ref_42","first-page":"1617","article-title":"Asymptotics of sample eigenstructure for a large dimensional spiked covariance model","volume":"17","author":"Paul","year":"2007","journal-title":"Statist. Sin."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.jmva.2015.05.009","article-title":"Robust spiked random matrices and a robust G-MUSIC estimator","volume":"140","author":"Couillet","year":"2015","journal-title":"J. Multivar. Anal."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2939","DOI":"10.1109\/TSP.2021.3076883","article-title":"Space-Time Adaptive Detection at Low Sample Support","volume":"69","author":"Robinson","year":"2021","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Combernoux, A., Pascal, F., Lesturgie, M., and Ginolhac, G. (2014, January 13\u201317). Performances of low rank detectors based on random matrix theory with application to STAP. Proceedings of the 2014 International Radar Conference, Lille, France.","DOI":"10.1109\/RADAR.2014.7060457"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1016\/S0378-4371(02)01499-1","article-title":"Noisy covariance matrices and portfolio optimization II","volume":"319","author":"Pafka","year":"2003","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1016\/j.physa.2004.05.079","article-title":"Estimated correlation matrices and portfolio optimization","volume":"343","author":"Pafka","year":"2004","journal-title":"Phys. A Stat. Mech. Table Its Appl."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1109\/LGRS.2008.2009553","article-title":"Local degrees of freedom of airborne array radar clutter for STAP","volume":"6","author":"Zhang","year":"2009","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"5353","DOI":"10.1109\/TSP.2008.929662","article-title":"On the Asymptotic Behavior of the Sample Estimates of Eigenvalues and Eigenvectors of Covariance Matrices","volume":"56","author":"Mestre","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"5113","DOI":"10.1109\/TIT.2008.929938","article-title":"Improved Estimation of Eigenvalues and Eigenvectors of Covariance Matrices Using Their Sample Estimates","volume":"54","author":"Mestre","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Couillet, R., and Debbah, M. (2011). Random Matrix Methods for Wireless Communications, Cambridge Univ. Press.","DOI":"10.1017\/CBO9780511994746"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1109\/TAES.2006.248216","article-title":"An approach to knowledge-aided covariance estimation","volume":"42","author":"Melvin","year":"2006","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.1109\/ICASSP.1996.543572","article-title":"The ARPA\/NAVY Mountaintop Program: Adaptive signal processing for airborne early warning radar","volume":"Volume 2","author":"Titi","year":"2002","journal-title":"Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/16\/3959\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:08:55Z","timestamp":1760141335000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/16\/3959"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,15]]},"references-count":53,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["rs14163959"],"URL":"https:\/\/doi.org\/10.3390\/rs14163959","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,15]]}}}