{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T09:29:21Z","timestamp":1766050161745,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,24]],"date-time":"2022-10-24T00:00:00Z","timestamp":1666569600000},"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":["62171229","BK20190772","20200020052005"],"award-info":[{"award-number":["62171229","BK20190772","20200020052005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["62171229","BK20190772","20200020052005"],"award-info":[{"award-number":["62171229","BK20190772","20200020052005"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010012","name":"National Aerospace Science Foundation of China","doi-asserted-by":"publisher","award":["62171229","BK20190772","20200020052005"],"award-info":[{"award-number":["62171229","BK20190772","20200020052005"]}],"id":[{"id":"10.13039\/501100010012","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, the design of low probability of intercept (LPI) radar waveforms considers not only the performance of passive interception systems (PISs), but also radar detection and resolution performance. Waveform design is an important considerations for the LPI ability of radar. Since information theory has a powerful performance-bound description ability from the perspective of information flow, LPI waveforms are designed in this paper within the constraints of the detection performance metrics of radar and PISs, both of which are measured by the Kullback\u2013Leibler divergence, and the resolution performance metric, which is measured by joint entropy. The designed optimization model of LPI waveforms can be solved using the sequential quadratic programming (SQP) method. Simulation results verify that the designed LPI waveforms not only have satisfactory target-detecting and resolution performance, but also have a superior low interception performance against PISs.<\/jats:p>","DOI":"10.3390\/e24111515","type":"journal-article","created":{"date-parts":[[2022,10,24]],"date-time":"2022-10-24T08:19:06Z","timestamp":1666599546000},"page":"1515","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Spatial Information-Theoretic Optimal LPI Radar Waveform Design"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1703-4218","authenticated-orcid":false,"given":"Jun","family":"Chen","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yidong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, 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":"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":[[2022,10,24]]},"reference":[{"key":"ref_1","unstructured":"Schrick, G., and Wiley, R.G. (1990, January 7\u201310). Interception of LPI radar signals. Proceedings of the IEEE International Conference on Radar, Arlington, VA, USA."},{"key":"ref_2","unstructured":"David, L. (2021). An Introduction to RF Stealth, SciTech. [2nd ed.]."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Lou, M., Zhong, T., Li, M., Li, X., Li, Z., Wu, J., and Yang, J. (2021, January 11\u201316). Low Probability of Intercept Waveform Optimization Method for Sar Imaging. Proceedings of the 2021 IEEE International Geoscience and Remote Sensing Symposium IGARSS, Brussels, Belgium.","DOI":"10.1109\/IGARSS47720.2021.9554227"},{"key":"ref_4","unstructured":"LeMieux, J.A., and Ingels, F.M. (1990, January 7\u201310). Analysis of FSK\/PSK modulated radar signals using Costas arrays and complementary Welti codes. Proceedings of the IEEE International Conference on Radar, Arlington, VA, USA."},{"key":"ref_5","unstructured":"Kim, I., Park, K., Song, M.K., Song, H., and Lee, J.Y. (2016\u20132, January 30). Design of LPI signals using optimal families of perfect polyphase sequences. Proceedings of the 2016 International Symposium on Information Theory and Its Applications (ISITA), Monterey, CA, USA."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Warnke, L., Correll, B., and Swanson, C.N. (2022). The density of Costas arrays decays exponentially. IEEE Trans. Inf. Theory, 1\u20137.","DOI":"10.1109\/TIT.2022.3202507"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Chen, J., Wang, F., and Zhou, J. (2015, January 14\u201319). The metrication of LPI radar waveforms based on the asymptotic spectral distribution of Wigner matrices. Proceedings of the 2015 IEEE International Symposium on Information Theory (ISIT), Hong Kong, China.","DOI":"10.1109\/ISIT.2015.7282471"},{"key":"ref_8","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_9","doi-asserted-by":"crossref","unstructured":"Xiao, Y., Deng, Z., and Wu, T. (2020). Information\u2013theoretic radar waveform design under the SINR constraint. Entropy, 22.","DOI":"10.3390\/e22101182"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"17184","DOI":"10.1109\/JSEN.2022.3192348","article-title":"Cooperative design for MIMO radar-communication spectral sharing system based on mutual information optimization","volume":"22","author":"Qian","year":"2022","journal-title":"IEEE Sens. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1109\/TSP.2017.2771726","article-title":"An efficient minorization maximization approach for MIMO radar waveform optimization via relative entropy","volume":"66","author":"Tang","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1109\/LSP.2017.2655879","article-title":"Information-theoretic optimal radar waveform design","volume":"24","author":"Zhu","year":"2017","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2918","DOI":"10.1109\/TSP.2022.3181346","article-title":"Generalized MBI algorithm for designing sequence set and mismatched filter bank with ambiguity function constraints","volume":"70","author":"Chen","year":"2022","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","unstructured":"Shu, Y., and Chen, Z. (2017, January 2\u20134). Evaluation and simulation of LPI radar signals\u2019 low probability of exploitation. Proceedings of the 2nd International Conference on Image, Vision and Computing (ICIVC), Chengdu, China."},{"key":"ref_15","first-page":"1","article-title":"Large-difference-scale target detection using a revised Bhattacharyya distance in SAR images","volume":"19","author":"Tang","year":"2022","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Hilali, A.E., Chergui, M., Wahbi, B.E., and Ayoub, F. (2021, January 3\u20135). A study of the relative operator entropy via some matrix versions of the Hellinger distance. Proceedings of the 4th International Conference on Advanced Communication Technologies and Networking (CommNet), Rabat, Morocco.","DOI":"10.1109\/CommNet52204.2021.9641881"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Nomura, R., and Yagi, H. (2021, January 12\u201320). Optimum intrinsic randomness rate with respect to f -divergences using the smooth min entropy. Proceedings of the IEEE International Symposium on Information Theory (ISIT), Melbourne, Australia.","DOI":"10.1109\/ISIT45174.2021.9517784"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/PL00011391","article-title":"A trust region method based on interior point techniques for nonlinear programming","volume":"89","author":"Byrd","year":"2000","journal-title":"Math. Program."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/11\/1515\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:01:35Z","timestamp":1760144495000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/11\/1515"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,24]]},"references-count":18,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["e24111515"],"URL":"https:\/\/doi.org\/10.3390\/e24111515","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,10,24]]}}}