{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T15:43:42Z","timestamp":1772207022945,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2022,11,28]],"date-time":"2022-11-28T00:00:00Z","timestamp":1669593600000},"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":["61901340"],"award-info":[{"award-number":["61901340"]}],"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":["61931016"],"award-info":[{"award-number":["61931016"]}],"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":["62071344"],"award-info":[{"award-number":["62071344"]}],"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":["2022KJXX-38"],"award-info":[{"award-number":["2022KJXX-38"]}],"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":["JB210212"],"award-info":[{"award-number":["JB210212"]}],"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":["2022TD-38"],"award-info":[{"award-number":["2022TD-38"]}],"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":["KGJ202X0X"],"award-info":[{"award-number":["KGJ202X0X"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Young Talent Starlet in Science and Technology in Shaanxi","award":["61901340"],"award-info":[{"award-number":["61901340"]}]},{"name":"Young Talent Starlet in Science and Technology in Shaanxi","award":["61931016"],"award-info":[{"award-number":["61931016"]}]},{"name":"Young Talent Starlet in Science and Technology in Shaanxi","award":["62071344"],"award-info":[{"award-number":["62071344"]}]},{"name":"Young Talent Starlet in Science and Technology in Shaanxi","award":["2022KJXX-38"],"award-info":[{"award-number":["2022KJXX-38"]}]},{"name":"Young Talent Starlet in Science and Technology in Shaanxi","award":["JB210212"],"award-info":[{"award-number":["JB210212"]}]},{"name":"Young Talent Starlet in Science and Technology in Shaanxi","award":["2022TD-38"],"award-info":[{"award-number":["2022TD-38"]}]},{"name":"Young Talent Starlet in Science and Technology in Shaanxi","award":["KGJ202X0X"],"award-info":[{"award-number":["KGJ202X0X"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["61901340"],"award-info":[{"award-number":["61901340"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["61931016"],"award-info":[{"award-number":["61931016"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["62071344"],"award-info":[{"award-number":["62071344"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2022KJXX-38"],"award-info":[{"award-number":["2022KJXX-38"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["JB210212"],"award-info":[{"award-number":["JB210212"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2022TD-38"],"award-info":[{"award-number":["2022TD-38"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["KGJ202X0X"],"award-info":[{"award-number":["KGJ202X0X"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Innovation Team of Shaanxi Province","award":["61901340"],"award-info":[{"award-number":["61901340"]}]},{"name":"Science and Technology Innovation Team of Shaanxi Province","award":["61931016"],"award-info":[{"award-number":["61931016"]}]},{"name":"Science and Technology Innovation Team of Shaanxi Province","award":["62071344"],"award-info":[{"award-number":["62071344"]}]},{"name":"Science and Technology Innovation Team of Shaanxi Province","award":["2022KJXX-38"],"award-info":[{"award-number":["2022KJXX-38"]}]},{"name":"Science and Technology Innovation Team of Shaanxi Province","award":["JB210212"],"award-info":[{"award-number":["JB210212"]}]},{"name":"Science and Technology Innovation Team of Shaanxi Province","award":["2022TD-38"],"award-info":[{"award-number":["2022TD-38"]}]},{"name":"Science and Technology Innovation Team of Shaanxi Province","award":["KGJ202X0X"],"award-info":[{"award-number":["KGJ202X0X"]}]},{"name":"National Radar Signal Processing Laboratory","award":["61901340"],"award-info":[{"award-number":["61901340"]}]},{"name":"National Radar Signal Processing Laboratory","award":["61931016"],"award-info":[{"award-number":["61931016"]}]},{"name":"National Radar Signal Processing Laboratory","award":["62071344"],"award-info":[{"award-number":["62071344"]}]},{"name":"National Radar Signal Processing Laboratory","award":["2022KJXX-38"],"award-info":[{"award-number":["2022KJXX-38"]}]},{"name":"National Radar Signal Processing Laboratory","award":["JB210212"],"award-info":[{"award-number":["JB210212"]}]},{"name":"National Radar Signal Processing Laboratory","award":["2022TD-38"],"award-info":[{"award-number":["2022TD-38"]}]},{"name":"National Radar Signal Processing Laboratory","award":["KGJ202X0X"],"award-info":[{"award-number":["KGJ202X0X"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Clutter suppression is a key problem for airborne radar, and space-time adaptive processing (STAP) is a core technology for clutter suppression and moving target detection. However, in practical applications, the non-uniform time-varying environments including clutter range dependence for non-side-looking radar lead to the training samples being unable to satisfy the sample requirements of STAP that they should be independent identical distributed (IID) and that their number should be greater than twice the system\u2019s degree of freedom (DOF). The lack of sufficient IID training samples causes difficulty in the convergence of STAP and further results in a serious degeneration of performance. To overcome this problem, this paper proposes a novel autoencoder neural network for clutter suppression with a unique matrix designed to be decoded and encoded. The main challenges are improving the accuracy of the estimation of the clutter-plus-noise covariance matrix (CNCM) for STAP convergence, designing the form of the data input to the network, and making the network successfully explored to the improvement of CNCM. For these challenges, the main proposed solutions include designing a unique matrix with a certain dimension and a series of covariance data selections and matrix transformations. Consequently, the proposed method compresses and retains the characteristics of the covariances, and abandons the deviations caused by the non-uniformity and the deficiency of training samples. Specifically, the proposed method firstly develops a unique matrix whose dimension is less than half of the DOF, meanwhile, it is based on a processing of the selected clutter-plus-noise covariances. Then, an autoencoder neural network with l2 regularization and the sparsity regularization is proposed for the unique matrix to be decoded and encoded. The training of the proposed autoencoder can be achieved by reducing the total loss function with the gradient descent iterations. Finally, an inverted processing for the autoencoder output is designed for the reconstruct ion of the clutter-plus-noise covariances. Simulation results are used to verify the effectiveness and advantages of the proposed method. It performs obviously superior clutter suppression for both side-looking and non-side-looking radars with strong clutter, and can deal with the insufficient and the non-uniform training samples. For these conditions, the proposed method provides the relatively narrowest and deepest IF notch. Furthermore, on average it improves the improvement factor (IF) by 10 dB more than the ADC, DW, JDL, and original STAP methods.<\/jats:p>","DOI":"10.3390\/rs14236021","type":"journal-article","created":{"date-parts":[[2022,11,28]],"date-time":"2022-11-28T07:01:30Z","timestamp":1669618890000},"page":"6021","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Autoencoder Neural Network-Based STAP Algorithm for Airborne Radar with Inadequate Training Samples"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2205-8759","authenticated-orcid":false,"given":"Jing","family":"Liu","sequence":"first","affiliation":[{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guisheng","family":"Liao","sequence":"additional","affiliation":[{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1865-6214","authenticated-orcid":false,"given":"Jingwei","family":"Xu","sequence":"additional","affiliation":[{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengqi","family":"Zhu","sequence":"additional","affiliation":[{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2596-8101","authenticated-orcid":false,"given":"Filbert H.","family":"Juwono","sequence":"additional","affiliation":[{"name":"Computer Science Program, University of Southampton Malaysia, Nusajaya 79100, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cao","family":"Zeng","sequence":"additional","affiliation":[{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7711","DOI":"10.1109\/JSEN.2020.2981398","article-title":"Automatic SAR Image Registration via Tsallis Entropy and Iterative Search Process","volume":"20","author":"Kang","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1109\/LGRS.2011.2167211","article-title":"A Neighborhood-Based Ratio Approach for Change Detection in SAR Images","volume":"9","author":"Gong","year":"2012","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"75","DOI":"10.2112\/SI102-010.1","article-title":"Land Subsidence Measurement of Jakarta Coastal Area Using Time Series Interferometry with Sentinel-1 SAR Data","volume":"102","author":"Hakim","year":"2020","journal-title":"J. Coast. Res."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Ward, J. (1998). Space-Time Adaptive Processing for Airborne Radar, MIT Lincoln Laboratory. Technical Report.","DOI":"10.1049\/ic:19980240"},{"key":"ref_5","unstructured":"Klemm, R. (2002). Principles of Space-Time Adaptive Processing, The Institution of Electrical Engineers."},{"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":"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_8","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1049\/el:19970243","article-title":"Estimation of the clutter rank in the case of subarraying for space-time adaptive processing","volume":"35","author":"Zhang","year":"1997","journal-title":"Electron. Lett."},{"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","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1049\/iet-rsn:20070162","article-title":"Foundation for mitigating range dependence in radar space-time adaptive processing","volume":"3","author":"Lapierre","year":"2009","journal-title":"IET Radar Sonar Navig."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1109\/7.845255","article-title":"Optimal and adaptive reduced-rank STAP","volume":"36","author":"Guerci","year":"2000","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1007\/BF02917165","article-title":"A framework of rank-reduced space-time adaptive processing for airborne radar and its applications","volume":"40","author":"Liao","year":"1997","journal-title":"Sci. China Ser. E Technol. Sci."},{"key":"ref_13","first-page":"27","article-title":"A comparative study of eigenspace based rank reduced STAP methods","volume":"28","author":"Zhang","year":"2000","journal-title":"Acta Electron. Sin."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1109\/78.554317","article-title":"Reduced rank adaptive filtering","volume":"45","author":"Goldstein","year":"1997","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","first-page":"426","article-title":"Improvement on the performance of the auxiliary channel STAP in the non-homogeneous environment","volume":"20","author":"Wang","year":"2004","journal-title":"J. Xidian Univ."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1049\/el:19960130","article-title":"Space-time joint processing method for simultaneous clutter and jamming rejection in airborne radar","volume":"32","author":"Wang","year":"1996","journal-title":"Electron. Lett."},{"key":"ref_17","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_18","doi-asserted-by":"crossref","first-page":"2222","DOI":"10.1016\/j.sigpro.2011.04.006","article-title":"Direct data domain STAP using sparse representation of clutter spectrum","volume":"91","author":"Sun","year":"2011","journal-title":"Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2756","DOI":"10.1109\/TAES.2017.2714938","article-title":"Sparsity-based STAP using alternating direction method with gain\/phase errors","volume":"53","author":"Yang","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_20","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_21","unstructured":"Lim, C.H., and Mulgrew, B. (2005, January 18\u201322). Filter banks based JDL with angle and separate Doppler compensation for airborne bistatic radar. Proceedings of the International Radar Symposium India, Bangalore, India."},{"key":"ref_22","unstructured":"Lapierre, F., Droogenbroeck, M.V., and Verly, J.G. (2003, January 6\u201310). New methods for handling the dependence of the clutter spectrum in non-sidelooking monostatic STAP radars. Proceedings of the IEEE Acoustics, Speech, and Signal Processing Conference, Hong Kong, China."},{"key":"ref_23","first-page":"85","article-title":"Registration-based range dependence compensation for bistatic STAP radars","volume":"1","author":"Lapierre","year":"2005","journal-title":"EURASIP J. Appl. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Lapierre, F., and Verly, J.G. (2005, January 9\u201312). Computationally-efficient range dependence compensation method for bistatic radar STAP. Proceedings of the IEEE International Radar Conference, Arlington, VA, USA.","DOI":"10.1109\/RADAR.2005.1435919"},{"key":"ref_25","unstructured":"Borsari, G.K. (1998, January 11\u201314). Mitigating effects on STAP processing caused by an inclined array. Proceedings of the 1998 IEEE Radar Conference, Dallas, TX, USA."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1049\/ip-rsn:20010557","article-title":"Doppler compensation in forward-looking STAP radar","volume":"148","author":"Kreyenkamp","year":"2001","journal-title":"IEE Proc. Radar Sonar Navig."},{"key":"ref_27","unstructured":"Himed, B., Zhang, Y., and Hajjari, A. (2002, January 25). STAP with angle-Doppler compensation for bistatic airborne radars. Proceedings of the IEEE Radar Conference, Long Beach, CA, USA."},{"key":"ref_28","unstructured":"Pearson, F., and Borsari, G. (2007, January 5\u20136). Simulation and analysis of adaptive interference suppression for bistatic surveillance radars. Proceedings of the Adaptive Sensor Array Process, Lexington, MA, USA."},{"key":"ref_29","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_30","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.dsp.2015.08.011","article-title":"Joint magnitude and phase constrained STAP approach","volume":"46","author":"Xu","year":"2015","journal-title":"Digit. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1006\/dspr.1998.0316","article-title":"Covariance matching estimation techniques for array signal processing applications","volume":"8","author":"Ottersten","year":"1998","journal-title":"Digit. Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1798","DOI":"10.1109\/TPAMI.2013.50","article-title":"Representation learning: A review and new perspectives","volume":"35","author":"Bengio","year":"2013","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_33","unstructured":"Goodfellow, I., Bengio, Y., and Courville, A. (2016). Deep Learning, MIT Press. Chapter 14."},{"key":"ref_34","unstructured":"Gregor, K., and Lecun, Y. (2010, January 21\u201324). Learning fast approximations of sparse coding. Proceedings of the 27th International Conference on International Conference on Machine Learning, Haifa, Israel."},{"key":"ref_35","first-page":"1","article-title":"Deep learning with Elastic Averaging SGD","volume":"28","author":"Zhang","year":"2015","journal-title":"Adv. Neural Inf. Process. Syst."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/23\/6021\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:28:13Z","timestamp":1760146093000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/23\/6021"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,28]]},"references-count":35,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["rs14236021"],"URL":"https:\/\/doi.org\/10.3390\/rs14236021","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,28]]}}}