{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:27:53Z","timestamp":1760243273572,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,8,28]],"date-time":"2022-08-28T00:00:00Z","timestamp":1661644800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["61531015"],"award-info":[{"award-number":["61531015"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Transmitting orthogonal waveforms are the basis for giving full play to the advantages of MIMO radar imaging technology, but the commonly used waveforms with the same frequency cannot meet the orthogonality requirement, resulting in serious coupling noise in traditional imaging methods and affecting the imaging effect. In order to effectively suppress the mutual coupling interference caused by non-orthogonal waveforms, a new non-orthogonal waveform MIMO radar imaging method based on deep learning is proposed in this paper: with the powerful nonlinear fitting ability of deep learning, the mapping relationship between the non-orthogonal waveform MIMO radar echo and ideal target image is automatically learned by constructing a deep imaging network and training on a large number of simulated training data. The learned imaging network can effectively suppress the coupling interference between non-ideal orthogonal waveforms and improve the imaging quality of MIMO radar. Finally, the effectiveness of the proposed method is verified by experiments with point scattering model data and electromagnetic scattering calculation data.<\/jats:p>","DOI":"10.3390\/a15090306","type":"journal-article","created":{"date-parts":[[2022,8,28]],"date-time":"2022-08-28T21:22:56Z","timestamp":1661721776000},"page":"306","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["MIMO Radar Imaging Method with Non-Orthogonal Waveforms Based on Deep Learning"],"prefix":"10.3390","volume":"15","author":[{"given":"Hongbing","family":"Li","sequence":"first","affiliation":[{"name":"School of Marine Science and Technology, Northwest Polytechnical University, Xi\u2019an 710072, China"},{"name":"Early Warning and Detection Department, Air Force Engineering University, Xi\u2019an 710051, China"}]},{"given":"Qunfei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwest Polytechnical University, Xi\u2019an 710072, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3009","DOI":"10.1109\/TGRS.2011.2119321","article-title":"Three-dimensional imaging of targets using colocated MIMO radar","volume":"49","author":"Ma","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1109\/JSTSP.2009.2038964","article-title":"Iterative adaptive approaches to MIMO radar imaging","volume":"4","author":"Roberts","year":"2010","journal-title":"IEEE J. Sel. Topics Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2236","DOI":"10.1109\/TAES.2015.140428","article-title":"MIMO radar imaging with imperfect carrier synchronization: A point spread function analysis","volume":"51","author":"Ding","year":"2015","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2628","DOI":"10.1109\/TGRS.2013.2263934","article-title":"MIMO-SAR: Opportunities and pitfalls","volume":"52","author":"Krieger","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3126","DOI":"10.1109\/TSP.2004.836530","article-title":"Polyphase code design for orthogonal netted radar systems","volume":"52","author":"Deng","year":"2004","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1070","DOI":"10.1109\/LSP.2003.821693","article-title":"Discrete frequency-coding waveform design for netted radar systems","volume":"11","author":"Deng","year":"2004","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2100","DOI":"10.1109\/TAES.2012.6237581","article-title":"Zero correlation zone sequence pair sets for MIMO radar","volume":"48","author":"Xu","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1644","DOI":"10.1109\/LGRS.2014.2303974","article-title":"MIMO SAR chirp modulation diversity waveform design","volume":"11","author":"Wang","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/s11045-015-0340-9","article-title":"MIMO radar OFDM chirp waveform diversity design with sparse modeling and joint optimization","volume":"28","author":"Cheng","year":"2017","journal-title":"Multidim. Syst. Sign. Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1556","DOI":"10.1109\/LGRS.2015.2412961","article-title":"A novel space-time coding scheme used for MIMO-SAR systems","volume":"12","author":"Wang","year":"2015","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3959","DOI":"10.1109\/TSP.2008.923197","article-title":"Signal synthesis and receiver design for MIMO radar imaging","volume":"56","author":"Li","year":"2008","journal-title":"IEEE Trans. on Signal Process."},{"key":"ref_12","first-page":"1","article-title":"MIMO-SAR waveforms separation in same frequency area based on virtual polarization filter","volume":"58","author":"Meng","year":"2015","journal-title":"Sci. China Inf. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1109\/LGRS.2014.2340898","article-title":"A novel scheme for ambiguous energy suppression in MIMO-SAR systems","volume":"12","author":"Wang","year":"2015","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_14","first-page":"5985","article-title":"MIMO Radar Imaging With Non-orthogonal Waveforms Based on Joint-Block Sparse Recovery","volume":"56","author":"Hu","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1049\/iet-rsn.2017.0149","article-title":"MIMO Radar Imaging Based on Multidimensional Linear Equations and Sparse Signal Recovery","volume":"12","author":"Ma","year":"2018","journal-title":"IET Radar Sonar Navig."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2168","DOI":"10.1109\/TIP.2014.2311735","article-title":"MIMO radar 3D imaging based on combined amplitude and total variation cost function with sequential order one negative exponential form","volume":"23","author":"Ma","year":"2014","journal-title":"IEEE Trans. Image Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3152","DOI":"10.1109\/JSEN.2018.2810705","article-title":"MIMO Radar 3D Imaging Based on Multi-dimensional Sparse Recovery and Signal Support Prior Information","volume":"18","author":"Hu","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_18","first-page":"107","article-title":"Synthetic aperture radar learning-imaging method based on data-driven technique and artificial intelligence","volume":"9","author":"Luo","year":"2020","journal-title":"J. Radars"},{"key":"ref_19","first-page":"467","article-title":"Overview of Radar Imaging Techniques Based on Deep Learning","volume":"19","author":"Zhang","year":"2021","journal-title":"Radar Sci. Technol."},{"key":"ref_20","first-page":"7096","article-title":"Inverse synthetic aperture radar imaging using complex-value deep neural network","volume":"2019","author":"Hu","year":"2019","journal-title":"J. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1203","DOI":"10.1109\/LGRS.2019.2943069","article-title":"Inverse synthetic aperture radar imaging using a fully convolutional neural network","volume":"17","author":"Hu","year":"2020","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1109\/LGRS.2018.2866567","article-title":"Enhanced radar imaging using a complex-valued convolutional neural network","volume":"16","author":"Gao","year":"2019","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1588","DOI":"10.1002\/mop.32186","article-title":"Resolution enhancement for inverse synthetic aperture radar images using a deep residual network","volume":"62","author":"Gao","year":"2020","journal-title":"Microw. Opt. Technol. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1109\/LGRS.2020.2965743","article-title":"Enhancing ISAR Resolution by a Generative Adversarial Network","volume":"18","author":"Qin","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wei, S., Liang, J., Wang, M., Zeng, X., Shi, J., and Zhang, X. (2020). CIST: An improved ISAR imaging method using convolution neural network. Remote Sens., 12.","DOI":"10.3390\/rs12162641"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"19222","DOI":"10.1109\/JSEN.2021.3090948","article-title":"Sparsity-Driven ISAR Imaging via Hierarchical Channel-Mixed Framework","volume":"21","author":"Liang","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3437","DOI":"10.1109\/JSEN.2020.3025053","article-title":"Deep Learning Approach for Sparse Aperture ISAR Imaging and Autofocusing Based on Complex-Valued ADMM-Net","volume":"21","author":"Li","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_28","first-page":"3073123","article-title":"AF-AMPNet: A Deep Learning Approach for Sparse Aperture ISAR Imaging and Autofocusing","volume":"60","author":"Wei","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2326","DOI":"10.3390\/rs13122326","article-title":"High-Resolution ISAR Imaging and Autofocusing via 2D-ADMM-Net","volume":"13","author":"Li","year":"2021","journal-title":"Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zhao, S., Ni, J., Liang, J., Xiong, S., and Luo, Y. (2021). End-to-End SAR Deep Learning Imaging Method Based on Sparse Optimization. Remote Sens., 13.","DOI":"10.3390\/rs13214429"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"7317","DOI":"10.1109\/TIP.2021.3104168","article-title":"TPSSI-Net: Fast and enhanced two-path iterative network for 3D SAR sparse imaging","volume":"30","author":"Wang","year":"2021","journal-title":"IEEE Trans. Image Processing"},{"key":"ref_32","first-page":"3110579","article-title":"MDLI-Net: Model-Driven Learning Imaging Network for High-Resolution Microwave Imaging With Large Rotating Angle and Sparse Sampling","volume":"60","author":"Hu","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1109\/8.785750","article-title":"A parametric model for synthetic aperture radar measurements","volume":"47","author":"Gerry","year":"1999","journal-title":"IEEE Trans. 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