{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T09:20:14Z","timestamp":1771665614682,"version":"3.50.1"},"reference-count":42,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2022,9,21]],"date-time":"2022-09-21T00:00:00Z","timestamp":1663718400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Special Fund for Research on National Major Research Instruments","award":["31727901"],"award-info":[{"award-number":["31727901"]}]},{"name":"Special Fund for Research on National Major Research Instruments","award":["62071045"],"award-info":[{"award-number":["62071045"]}]},{"name":"Special Fund for Research on National Major Research Instruments","award":["61625103"],"award-info":[{"award-number":["61625103"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["31727901"],"award-info":[{"award-number":["31727901"]}],"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":["62071045"],"award-info":[{"award-number":["62071045"]}],"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":["61625103"],"award-info":[{"award-number":["61625103"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Integrated radar and communications (IRC) technology has become very important for civil and military applications in recent years, and IRC waveform design is a major challenge for IRC development. In this paper, we focus on the IRC waveform design based on the multi-symbol orthogonal frequency division multiplexing (OFDM) technique. In view of the defects resulting from high peak-to-mean envelope power ratios (PMEPRs) and high range sidelobes in IRC systems, an intelligent and effective IRC waveform design method jointly optimized with the PMEPR and peak-to-sidelobe ratio (PSLR) is proposed. Firstly, a flexible tone reservation (TR)-based IRC waveform structure is applied in both temporal and frequency domains, i.e., multi-symbol OFDM waveform. Secondly, the optimization problem considering PMEPR and PSLR and extending them to the Lp-norm form is reformulated. Then, the conjugate gradient of the objective function is analytically derived and the conjugate gradient algorithm (CGA) is presented to simultaneously improve the PMEPR and PSLR. Finally, the simulation results show that the proposed algorithm can efficiently generate IRC waveforms with an excellent PMEPR, PSLR, radar signal-to-noise ratio (SNR), and bit error rate (BER) performance.<\/jats:p>","DOI":"10.3390\/rs14194705","type":"journal-article","created":{"date-parts":[[2022,9,22]],"date-time":"2022-09-22T23:07:55Z","timestamp":1663888075000},"page":"4705","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Integrated Radar and Communications Waveform Design Based on Multi-Symbol OFDM"],"prefix":"10.3390","volume":"14","author":[{"given":"Juan","family":"Rong","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China"},{"name":"Key Laboratory of Electronic and Information Technology in Satellite Navigation, Ministry of Education, Beijing 100081, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1158-2862","authenticated-orcid":false,"given":"Feifeng","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Electronic and Information Technology in Satellite Navigation, Ministry of Education, Beijing 100081, China"},{"name":"School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China"}]},{"given":"Yingjie","family":"Miao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Electronic and Information Technology in Satellite Navigation, Ministry of Education, Beijing 100081, China"},{"name":"School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1016\/j.telpol.2019.04.001","article-title":"The evolving 5G case study in spectrum management and industrial policy","volume":"43","author":"Frieden","year":"2019","journal-title":"Telecommun. Policy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1236","DOI":"10.1109\/JPROC.2011.2131110","article-title":"Waveform design and signal processing aspects for fusion of wireless communications and radar sensing","volume":"99","author":"Sturm","year":"2011","journal-title":"Proc. IEEE"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1241","DOI":"10.1109\/TAES.2019.2899797","article-title":"A mmWave automotive joint radar-communications system","volume":"55","author":"Dokhanchi","year":"2019","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1572","DOI":"10.1109\/LWC.2020.2997959","article-title":"On range sidelobe reduction for dual-functional radar-communication waveforms","volume":"9","author":"Liu","year":"2020","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2174","DOI":"10.1109\/LCOMM.2017.2723890","article-title":"Adaptive OFDM integrated radar and communications waveform design based on information theory","volume":"21","author":"Liu","year":"2017","journal-title":"IEEE Commun. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6979","DOI":"10.1109\/TWC.2022.3153606","article-title":"Designing low-PAPR waveform for OFDM-based radCom systems","volume":"21","author":"Huang","year":"2022","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.23919\/JCC.2020.01.001","article-title":"Joint radar and communication: A survey","volume":"17","author":"Feng","year":"2020","journal-title":"China Commun."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1431","DOI":"10.1109\/TMTT.2007.900343","article-title":"Ultra-wideband multifunctional communications\/radar system","volume":"55","author":"Saddik","year":"2007","journal-title":"IEEE Trans. Microw. Theory Techn."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1109\/TAES.2010.5545182","article-title":"BIntrapulse radar-embedded communications","volume":"46","author":"Blunt","year":"2010","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1567","DOI":"10.1109\/SURV.2013.021313.00164","article-title":"Peak-to-average power ratio reduction in OFDM systems: A survey and taxonomy","volume":"15","author":"Rahmatallah","year":"2013","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1109\/MWC.2005.1421929","article-title":"An overview of peak-to-average power ratio reduction techniques for multicarrier transmission","volume":"12","author":"Han","year":"2005","journal-title":"IEEE Wirel. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1049\/el:20020175","article-title":"Peak-to-average power reduction for OFDM by repeated clipping and frequency domain filtering","volume":"38","author":"Armstrong","year":"2002","journal-title":"Electron. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1891","DOI":"10.1109\/TCOMM.2013.021913.110867","article-title":"Simplified approach to optimized iterative clipping and filtering for PAPR reduction of OFDM signal","volume":"61","author":"Zhu","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1109\/TVT.2005.863417","article-title":"IMD reduction with SLM and PTS to improve the error probability performance of nonlinearly distorted OFDM signals","volume":"55","author":"Rodrigues","year":"2006","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1109\/TCOMM.2010.02.090055","article-title":"Novel sequence design for low-PMEPR and high-code-rate OFDM systems","volume":"58","author":"Huang","year":"2010","journal-title":"IEEE Trans. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1049\/ip-rsn:20030263","article-title":"Multicarrier radar signals with low peak-to-mean envelope power ratio","volume":"150","author":"Mozeson","year":"2003","journal-title":"IEE Proc.-Radar Sonar Navig."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"184053","DOI":"10.1109\/ACCESS.2019.2960658","article-title":"Waveform design for dual-function radar-communication system with golay block coding","volume":"7","author":"Li","year":"2019","journal-title":"IEEE Access"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Jiao, Y.Z., Liu, X.J., and Wang, X.A. (2008, January 10\u201312). A novel tone reservation scheme with fast convergence for PAPR reduction in OFDM systems. Proceedings of the 2008 5th IEEE Consumer Communications and Networking Conference, Las Vegas, NV, USA.","DOI":"10.1109\/ccnc08.2007.95"},{"key":"ref_19","unstructured":"Tellado, J. (1999). Peak to Average Power Reduction for Multicarrier Modulation. [Ph.D. Thesis, Stanford University]."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1109\/TSP.2003.821110","article-title":"An active-set approach for OFDM PAR reduction via tone reservation","volume":"52","author":"Krongold","year":"2004","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5373","DOI":"10.1109\/TVT.2014.2378811","article-title":"Tone reservation technique based on peak-windowing residual noise for PAPR reduction in OFDM systems","volume":"64","author":"Hou","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1675","DOI":"10.1109\/TVT.2007.907282","article-title":"Analysis of clipping noise and tone reservation algorithms for peak reduction in OFDM systems","volume":"57","author":"Wang","year":"2008","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Rong, J., Liu, F., and Miao, Y. (2022). High-efficiency optimization algorithm of PMEPR for OFDM integrated radar and communication waveform based on conjugate gradient. Remote Sens., 14.","DOI":"10.3390\/rs14071715"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3658","DOI":"10.1109\/TGRS.2013.2274593","article-title":"PAPR-constrained pareto-optimal waveform design for OFDM-STAP Radar","volume":"52","author":"Sen","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zhao, J., Huo, K., and Li, X. (2014, January 19\u201323). A chaos-based phase-coded OFDM signal for joint radar-communication systems. Proceedings of the 2014 12th International Conference on Signal Processing (ICSP), Hangzhou, China.","DOI":"10.1109\/ICOSP.2014.7015343"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Takase, H., and Shinriki, M. (2014, January 16\u201318). A dual-use system for radar and communication with complete complementary codes. Proceedings of the 2014 15th International Radar Symposium (IRS), Gdansk, Poland.","DOI":"10.1109\/IRS.2014.6869268"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Hu, L., Du, Z., and Xue, G. (2014, January 5\u20138). Radar-communication integration based on OFDM signal. Proceedings of the 2014 IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC), Guilin, China.","DOI":"10.1109\/ICSPCC.2014.6986232"},{"key":"ref_28","first-page":"7624","article-title":"Range sidelobe suppression for OFDM integrated radar and communication signal","volume":"2019","author":"Zuo","year":"2019","journal-title":"J. Eng."},{"key":"ref_29","first-page":"1662","article-title":"Range sidelobe suppression of integrated radar and communication signals based on OFDM","volume":"36","author":"Zuo","year":"2020","journal-title":"J. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1109\/LCOMM.2020.3033119","article-title":"Tunable filter design for integrated radar and communication waveforms","volume":"25","author":"Jiang","year":"2021","journal-title":"IEEE Commun. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1049\/iet-rsn:20080106","article-title":"Orthogonal frequency-division multiplexing radar signal design with optimised ambiguity function and low peak-to-average power ratio","volume":"3","author":"Sebt","year":"2009","journal-title":"IET Radar Sonar Navig."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"9840172","DOI":"10.1155\/2017\/9840172","article-title":"Radar communication integrated waveform design based on OFDM and circular shift sequence","volume":"2017","author":"Li","year":"2017","journal-title":"Math. Probl. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"990","DOI":"10.1109\/TVT.2005.863353","article-title":"On the design and performance analysis of multisymbol encapsulated OFDM systems","volume":"55","author":"Wang","year":"2006","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Janaaththanan, S., Kasparis, C., and Evans, B.G. (2008, January 11\u201314). A gradient based algorithm for PAPR reduction of OFDM using tone reservation technique. Proceedings of the VTC Spring 2008-IEEE Vehicular Technology Conference, Marina Bay, Singapore.","DOI":"10.1109\/VETECS.2008.315"},{"key":"ref_35","unstructured":"Zhang, X. (2004). Matrix Analysis and Applications, Tsinghua University Press."},{"key":"ref_36","unstructured":"Ding, L., and Geng, F. (2002). Principle of Radar, Xidian University Press. [3rd ed.]."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1298","DOI":"10.1109\/TWC.2008.060862","article-title":"Derivation of PAPR distribution for OFDM wireless systems based on extreme value theory","volume":"7","author":"Jiang","year":"2008","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.sigpro.2018.01.006","article-title":"Designing PAR-constrained periodic\/aperiodic sequence via the gradient-based method","volume":"147","author":"Liang","year":"2018","journal-title":"Signal Process."},{"key":"ref_39","first-page":"35","article-title":"Note sur la convergence de directions conjug\u00e8es","volume":"16","author":"Polak","year":"1969","journal-title":"Rev. Fr. Inform. Rech. Oper."},{"key":"ref_40","unstructured":"Nee, R.V., and Prasad, R. (2000). OFDM for Wireless Multimedia Communications, Artech House."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1049\/iet-rsn.2019.0477","article-title":"Parameter estimation of underwater impulsive noise with the class B model","volume":"14","author":"Zhang","year":"2020","journal-title":"IET Radar Sonar Navig."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Mahmood, A., and Chitre, M. (2015, January 18\u201321). Modeling colored impulsive noise by Markov chains and alpha-stable processes. Proceedings of the OCEANS 2015, Genova, Italy.","DOI":"10.1109\/OCEANS-Genova.2015.7271550"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/19\/4705\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:36:17Z","timestamp":1760142977000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/19\/4705"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,21]]},"references-count":42,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["rs14194705"],"URL":"https:\/\/doi.org\/10.3390\/rs14194705","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,21]]}}}