{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T00:38:47Z","timestamp":1774053527973,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,3,16]],"date-time":"2018-03-16T00:00:00Z","timestamp":1521158400000},"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":["61371170"],"award-info":[{"award-number":["61371170"]}],"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":["61671239"],"award-info":[{"award-number":["61671239"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["NS2016038"],"award-info":[{"award-number":["NS2016038"]}],"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":["NP2015404"],"award-info":[{"award-number":["NP2015404"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, the problem of low probability of intercept (LPI)-based radar waveform design for distributed multiple-radar system (DMRS) is studied, which consists of multiple radars coexisting with a wireless communication system in the same frequency band. The primary objective of the multiple-radar system is to minimize the total transmitted energy by optimizing the transmission waveform of each radar with the communication signals acting as interference to the radar system, while meeting a desired target detection\/characterization performance. Firstly, signal-to-clutter-plus-noise ratio (SCNR) and mutual information (MI) are used as the practical metrics to evaluate target detection and characterization performance, respectively. Then, the SCNR- and MI-based optimal radar waveform optimization methods are formulated. The resulting waveform optimization problems are solved through the well-known bisection search technique. Simulation results demonstrate utilizing various examples and scenarios that the proposed radar waveform design schemes can evidently improve the LPI performance of DMRS without interfering with friendly communications.<\/jats:p>","DOI":"10.3390\/e20030197","type":"journal-article","created":{"date-parts":[[2018,3,16]],"date-time":"2018-03-16T04:22:59Z","timestamp":1521174179000},"page":"197","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Low Probability of Intercept-Based Radar Waveform Design for Spectral Coexistence of Distributed Multiple-Radar and Wireless Communication Systems in Clutter"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2507-2954","authenticated-orcid":false,"given":"Chenguang","family":"Shi","sequence":"first","affiliation":[{"name":"Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fei","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sana","family":"Salous","sequence":"additional","affiliation":[{"name":"School of Engineering and Computing Sciences, Durham University, Durham DH1 3DE, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianjiang","family":"Zhou","sequence":"additional","affiliation":[{"name":"Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1109\/TSP.2005.862813","article-title":"Spatial diversity in radars\u2014Models and detection performance","volume":"54","author":"Fisher","year":"2006","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1109\/MSP.2008.4408448","article-title":"MIMO radar with widely separated antennas","volume":"25","author":"Haimovich","year":"2008","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6417","DOI":"10.1109\/TSP.2016.2607147","article-title":"Joint beam selection and power allocation for multiple target tracking in netted colocated MIMO radar system","volume":"64","author":"Yan","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1109\/TAES.2014.140093","article-title":"A new radar waveform design algorithm with improved feasibility for spectral coexistence","volume":"51","author":"Aubry","year":"2015","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1049\/iet-rsn.2016.0312","article-title":"Spectrum sharing between communications and ATC radar systems","volume":"11","author":"Wang","year":"2017","journal-title":"IET Radar Sonar Navig."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Li, B., and Petropulu, A. (2017). Joint transmit designs for co-existence of MIMO wireless communications and sparse sensing radars in clutter. IEEE Trans. Aerosp. Electron. Syst.","DOI":"10.1109\/TAES.2017.2717518"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Labib, M., Reed, J.H., Martone, A.F., and Zaghloul, A.I. (July, January 26). A game-theoretic approach for radar and LTE systems coexistence in the unlicensed band. Proceedings of the 2016 USNC-URSI Radio Science Meeting, Fajardo, Puerto Rico.","DOI":"10.1109\/USNC-URSI.2016.7588490"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2139","DOI":"10.1109\/TCOMM.2005.860047","article-title":"The effect of narrowband interference on wideband wireless communication systems","volume":"53","author":"Giorgetti","year":"2005","journal-title":"IEEE Trans. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1109\/LSP.2016.2532739","article-title":"Forcing multiple spectral compatibility constraints in radar waveforms","volume":"23","author":"Aubry","year":"2016","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1109\/MAES.2016.150216","article-title":"Optimization theory-based radar waveform design for spectrally dense environments","volume":"31","author":"Aubry","year":"2016","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1268","DOI":"10.1109\/JSAC.2009.090922","article-title":"A stochastic geometry approach to coexistence in heterogeneous wireless networks","volume":"27","author":"Pinto","year":"2009","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1109\/COMST.2016.2624939","article-title":"Modeling and analysis of cellular networks using stochastic geometry: A tutorial","volume":"19","author":"ElSawy","year":"2017","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_13","unstructured":"Gogineni, S., Rangaswamy, M., and Nehorai, A. (May, January 29). Multi-modal OFDM waveform design. Proceedings of the IEEE Radar Conference (RadarConf), Ottawa, ON, Canada."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Turlapaty, A., and Jin, Y.W. (2014, January 19\u201323). A joint design of transmit waveforms for radar and communication systems in coexistence. Proceedings of the IEEE Radar Conference (RadarConf), Cincinnati, OH, USA.","DOI":"10.1109\/RADAR.2014.6875606"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Bica, M., and Koivunen, V. (2017, January 8\u201312). Delay estimation method for coexisting radar and wireless communication systems. Proceedings of the IEEE Radar Conference (RadarConf), Seattle, WA, USA.","DOI":"10.1109\/RADAR.2017.7944455"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1109\/TSP.2015.2483485","article-title":"Inner bounds on performance of radar and communications co-existence","volume":"64","author":"Chiriyath","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Zheng, L., Lpos, M., Wang, X.D., and Grossi, E. (2017). Joint design of overlaid communication systems and pulsed radars. IEEE Trans. Signal Process.","DOI":"10.1109\/TSP.2017.2755603"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Shi, C.G., Wang, F., Zhou, J.J., and Zhang, H. (2015, January 19\u201324). Security information factor based low probability of identification in distributed multiple-radar system. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brisbane, Australia.","DOI":"10.1109\/ICASSP.2015.7178665"},{"key":"ref_19","first-page":"1","article-title":"A novel resource scheduling method of netted radars based on Markov decision process during target tracking in clutter","volume":"16","author":"Zhang","year":"2016","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Shi, C.G., Zhou, J.J., and Wang, F. (2016, January 2\u20136). LPI based resource management for target tracking in distributed radar network. Proceedings of the IEEE Radar Conference (RadarConf), Philadelphia, PA, USA.","DOI":"10.1109\/RADAR.2016.7485222"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1049\/iet-rsn.2016.0362","article-title":"Low probability of intercept based multicarrier radar jamming power allocation for joint radar and wireless communications systems","volume":"11","author":"Shi","year":"2017","journal-title":"IET Radar Sonar Navig."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"70","DOI":"10.4218\/etrij.16.0114.1230","article-title":"Robust transmission waveform design for distributed multiple-radar systems based on low probability of intercept","volume":"38","author":"Shi","year":"2016","journal-title":"ETRI J."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.1109\/ACCESS.2015.2473169","article-title":"Friendly spectrally shaped radar waveform with legacy communication systems for shared access and spectrum management","volume":"3","author":"Romero","year":"2015","journal-title":"IEEE Access"},{"key":"ref_24","unstructured":"Huang, K.W., Bica, M., Mitra, U., and Koivunen, V. (2015, January 10\u201315). Radar waveform design in spectrum sharing environment: Coexistence and cognition. Proceedings of the IEEE Radar Conference (RadarConf), Arlington, VA, USA."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Bica, M., Huang, K.W., Mitra, U., and Koivunen, V. (2015, January 6\u201310). Opportunistic radar waveform design in joint radar and cellular communication systems. Proceedings of the IEEE Global Communications Conference (GLOBECOM), San Diego, CA, USA.","DOI":"10.1109\/GLOCOM.2015.7417624"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Bica, M., Huang, K.W., Koivunen, V., and Mitra, U. (2016, January 20\u201325). Mutual information based radar waveform design for joint radar and cellular communication systems. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, China.","DOI":"10.1109\/ICASSP.2016.7472362"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Shi, C.G., Salous, S., Wang, F., and Zhou, J.J. (2016). Low probability of intercept based adaptive radar waveform optimization in signal dependent clutter for joint radar and cellular communication systems. EURASIP J. Adv. Signal Process.","DOI":"10.1186\/s13634-016-0411-6"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1316","DOI":"10.1109\/TSP.2017.2770086","article-title":"Power minimization based robust OFDM radar waveform design for radar and communication systems in coexistence","volume":"66","author":"Shi","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1109\/TAES.2011.5751234","article-title":"Theory and application of SNR and mutual information matched illumination waveforms","volume":"47","author":"Romero","year":"2011","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1578","DOI":"10.1109\/18.259642","article-title":"Information theory and radar waveform design","volume":"39","author":"Bell","year":"1993","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1374","DOI":"10.1109\/TAES.2013.6494422","article-title":"Adaptive distributed MIMO radar waveform optimization based on mutual information","volume":"49","author":"Chen","year":"2013","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1957","DOI":"10.1109\/TCOMM.2011.060911.100581","article-title":"Direct sequence and time-hopping sequence designs for narrowband interference mitigation in impulse radio UWB systems","volume":"59","author":"Shao","year":"2011","journal-title":"IEEE Trans. Commun."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Giorgetti, A. (2010, January 7\u201310). Interference mitigation technique by sequence design in UWB cognitive radio. Proceedings of the 3rd International Symposium on Applied Sciences in Biomedical and Communication Technologies (ISABEL 2010), Roma, Italy.","DOI":"10.1109\/ISABEL.2010.5702853"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1732","DOI":"10.1109\/JQE.2004.836811","article-title":"Ambiguity functions of laser-based chaotic radar","volume":"40","author":"Lin","year":"2004","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1109\/TAES.2007.4383592","article-title":"Optimal radar signal for detection in clutter","volume":"43","author":"Kay","year":"2007","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1859","DOI":"10.1049\/iet-com.2013.1054","article-title":"Minimax robust jamming techniques based on signal-to-interference-plus-noise ratio and mutual information","volume":"8","author":"Wang","year":"2014","journal-title":"IET Commun."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/3\/197\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:57:18Z","timestamp":1760194638000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/3\/197"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,16]]},"references-count":36,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,3]]}},"alternative-id":["e20030197"],"URL":"https:\/\/doi.org\/10.3390\/e20030197","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,16]]}}}