{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T15:55:29Z","timestamp":1772726129517,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T00:00:00Z","timestamp":1724371200000},"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>The orthogonal frequency-division multiplexing (OFDM) mode with a linear frequency modulation (LFM) signal as the baseband waveform has been widely studied and applied in multiple-input multiple-output (MIMO) radar systems. However, its high sidelobe levels after pulse compression affect the target detection of radar systems. For this paper, theoretical analysis was performed, to investigate the causes of high sidelobe levels in OFDM-LFM waveforms, and a novel waveform optimization design method based on deep neural networks is proposed. This method utilizes the classic ResNeXt network to construct dual-channel neural networks, and a new loss function is employed to design the phase and bandwidth of the OFDM-LFM waveforms. Meanwhile, the optimization factor is exploited, to address the optimization problem of the peak sidelobe levels (PSLs) and integral sidelobe levels (ISLs). Our numerical results verified the correctness of the theoretical analysis and the effectiveness of the proposed method. The designed OFDM-LFM waveforms exhibited outstanding performance in pulse compression and improved the detection performance of the radar.<\/jats:p>","DOI":"10.3390\/s24175471","type":"journal-article","created":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T12:58:07Z","timestamp":1724417887000},"page":"5471","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Novel Waveform Optimization Method for Orthogonal-Frequency Multiple-Input Multiple-Output Radar Based on Dual-Channel Neural Networks"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6386-8497","authenticated-orcid":false,"given":"Meng","family":"Xia","sequence":"first","affiliation":[{"name":"School of Communication and Information Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenrong","family":"Gong","sequence":"additional","affiliation":[{"name":"School of Communication and Information Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lichao","family":"Yang","sequence":"additional","affiliation":[{"name":"Science and Technology on Communication Information Security Control Laboratory, Jiaxing 314033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,23]]},"reference":[{"key":"ref_1","first-page":"886","article-title":"Design Principles of MIMO Radar Detectors","volume":"44","author":"Lops","year":"2008","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Pan, J., Zheng, Z., Zhao, D., Yan, K., Nie, J., Zhou, B., and Fang, G. (2023). A Multi-Target Detection Method Based on Improved U-Net for UWB MIMO Through-Wall Radar. Remote Sens., 15.","DOI":"10.3390\/rs15133434"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Rojhani, N., and Shaker, G. (2024). Comprehensive Review: Effectiveness of MIMO and Beamforming Technologies in Detecting Low RCS UAVs. Remote Sens., 16.","DOI":"10.3390\/rs16061016"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3396","DOI":"10.1109\/TSP.2015.2422680","article-title":"Joint Range and Angle Estimation Using MIMO Radar With Frequency Diverse Array","volume":"63","author":"Xu","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5230112","DOI":"10.1109\/TGRS.2022.3184709","article-title":"An Advanced Scheme for Range Ambiguity Suppression of Spaceborne SAR Based on Blind Source Separation","volume":"60","author":"Chang","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1109\/TAES.2008.4516997","article-title":"Transmit beamforming for MIMO radar systems using signal cross-correlation","volume":"44","author":"Fuhrmann","year":"2008","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1109\/TSP.2013.2288086","article-title":"MIMO Radar Waveform Design with Constant Modulus and Similarity Constraints","volume":"62","author":"Cui","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2168","DOI":"10.1109\/TSP.2015.2505667","article-title":"Dual-Function Radar-Communications: Information Embedding Using Sidelobe Control and Waveform Diversity","volume":"64","author":"Hassanien","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1109\/MSP.2007.904812","article-title":"MIMO Radar with Colocated Antennas","volume":"24","author":"Li","year":"2007","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1109\/TAES.2007.357137","article-title":"MIMO radar waveform design based on mutual information and minimum mean-square error estimation","volume":"43","author":"Yang","year":"2007","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1415","DOI":"10.1109\/TSP.2009.2012562","article-title":"New Algorithms for Designing Unimodular Sequences with Good Correlation Properties","volume":"57","author":"Stoica","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3998","DOI":"10.1109\/TSP.2015.2425808","article-title":"Optimization Methods for Designing Sequences with Low Autocorrelation Sidelobes","volume":"63","author":"Song","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3955","DOI":"10.1109\/TSP.2016.2543207","article-title":"MIMO Radar Beampattern Design via PSL\/ISL Optimization","volume":"64","author":"Aubry","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4207","DOI":"10.1109\/TSP.2018.2847636","article-title":"Constant Modulus MIMO Radar Waveform Design with Minimum Peak Sidelobe Transmit Beampattern","volume":"66","author":"Fan","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1274","DOI":"10.1109\/TAES.2020.3046086","article-title":"Adaptive Transmit Waveform Design Using Multitone Sinusoidal Frequency Modulation","volume":"57","author":"Hague","year":"2021","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1116","DOI":"10.1049\/rsn2.12247","article-title":"Optimisation of practically constrained waveforms for rician target detection with multiple-input-multiple-output radar","volume":"16","author":"Wang","year":"2022","journal-title":"IET Radar Sonar Navig."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1109\/TAES.2021.3103560","article-title":"Joint Design of Radar Waveform and Detector via End-to-End Learning with Waveform Constraints","volume":"58","author":"Jiang","year":"2022","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_18","first-page":"1007","article-title":"MIMO Radar Transmit Beampattern Shaping for Spectrally Dense Environments","volume":"59","author":"Raei","year":"2023","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1319","DOI":"10.1049\/iet-rsn.2015.0642","article-title":"Orthogonal frequency division multiplexing linear frequency modulation signal design with optimised pulse compression property of spatial synthesised signals","volume":"10","author":"Li","year":"2016","journal-title":"IET Radar Sonar Navig."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1109\/LGRS.2016.2639826","article-title":"Correlated LFM Waveform Set Design for MIMO Radar Transmit Beampattern","volume":"14","author":"Li","year":"2017","journal-title":"IEEE Geosci. Remote. Sens. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"7501204","DOI":"10.1109\/LSENS.2021.3129081","article-title":"Ambiguity Function Analysis for Orthogonal-LFM Waveform Based Multistatic Radar","volume":"5","author":"Dash","year":"2021","journal-title":"IEEE Sens. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1348","DOI":"10.1109\/ACCESS.2022.3233103","article-title":"Waveform Design and DoA-DoD Estimation of OFDM-LFM Signal Based on SDFnT for MIMO Radar","volume":"11","author":"Wang","year":"2023","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Wang, S., He, F., and Dong, Z. (2024). A Novel Intrapulse Beamsteering SAR Imaging Mode Based on OFDM-Chirp Signals. Remote Sens., 16.","DOI":"10.3390\/rs16010126"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3500105","DOI":"10.1109\/LGRS.2023.3331716","article-title":"Joint Design of OFDM-LFM Waveforms and Receive Filter for MIMO Radar in Spatial Heterogeneous Clutter","volume":"21","author":"Ding","year":"2024","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2196","DOI":"10.1109\/TGRS.2017.2776357","article-title":"SAR Automatic Target Recognition Based on Multiview Deep Learning Framework","volume":"56","author":"Pei","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"8983","DOI":"10.1109\/TGRS.2019.2923988","article-title":"Dense Attention Pyramid Networks for Multi-Scale Ship Detection in SAR Images","volume":"57","author":"Cui","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5751","DOI":"10.1109\/TGRS.2019.2901945","article-title":"A Deep Learning Method for Change Detection in Synthetic Aperture Radar Images","volume":"57","author":"Li","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Wu, Z., Hou, B., Ren, B., Ren, Z., Wang, S., and Jiao, L. (2021). A Deep Detection Network Based on Interaction of Instance Segmentation and Object Detection for SAR Images. Remote Sens., 13.","DOI":"10.3390\/rs13132582"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Li, H., and Zhang, Q. (2022). MIMO Radar Imaging Method with Non-Orthogonal Waveforms Based on Deep Learning. Algorithms, 15.","DOI":"10.3390\/a15090306"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"13704","DOI":"10.1109\/JSEN.2021.3071941","article-title":"CNN-Based Regional People Counting Algorithm Exploiting Multi-Scale Range-Time Maps with an IR-UWB Radar","volume":"21","author":"Bao","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3500205","DOI":"10.1109\/LGRS.2022.3229141","article-title":"Ship Detection Based on Faster R-CNN Using Range-Compressed Airborne Radar Data","volume":"20","author":"Loran","year":"2023","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Liang, R., and Cen, Y. (2024). Radar Signal Classification with Multi-Frequency Multi-Scale Deformable Convolutional Networks and Attention Mechanisms. Remote Sens., 44.","DOI":"10.3390\/rs16081431"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1184","DOI":"10.1109\/TAES.2020.3037406","article-title":"Designing Unimodular Waveform(s) for MIMO Radar by Deep Learning Method","volume":"57","author":"Hu","year":"2021","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"7498","DOI":"10.1109\/JSEN.2020.3046291","article-title":"Robust DOA Estimation Method for MIMO Radar via Deep Neural Networks","volume":"21","author":"Cong","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3503405","DOI":"10.1109\/LGRS.2024.3368446","article-title":"MIMO Radar Waveform Design for Range-ISL Optimization via Iterative Deep Unfolding Network","volume":"21","author":"Zhao","year":"2024","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (2016, January 27\u201330). Deep Residual Learning for Image Recognition. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition 2016, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Xie, S., Girshick, R., Doll\u00e1r, P., Tu, Z., and He, K. (2017, January 21\u201326). Aggregated Residual Transformations for Deep Neural Networks. Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition 2017, Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.634"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/17\/5471\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:42:25Z","timestamp":1760110945000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/17\/5471"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,23]]},"references-count":37,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["s24175471"],"URL":"https:\/\/doi.org\/10.3390\/s24175471","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,23]]}}}