{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:42:37Z","timestamp":1760236957709,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,1,31]],"date-time":"2020-01-31T00:00:00Z","timestamp":1580428800000},"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":["61661032, 61461030, 61761030"],"award-info":[{"award-number":["61661032, 61461030, 61761030"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Young Natural Science Foundation of Jiangxi Province","award":["20181BAB202002"],"award-info":[{"award-number":["20181BAB202002"]}]},{"DOI":"10.13039\/501100019079","name":"Postdoctoral Science Foundation of Jiangxi Province","doi-asserted-by":"publisher","award":["2017KY36"],"award-info":[{"award-number":["2017KY36"]}],"id":[{"id":"10.13039\/501100019079","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2017M622102, 2017M622103"],"award-info":[{"award-number":["2017M622102, 2017M622103"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper considers the design of a desired transmit beampattern under the good ambiguity function constraint using a correlated linear frequency modulation-phase coded (LFM-PC) waveform set in multiple-input-multiple-output (MIMO) radar. Different from most existing beampattern design approaches, we propose using the LFM-PC waveform set to conquer the challenging problem of synthesizing waveforms with constant-envelope and easy-generation properties, and, meanwhile, solve the hard constraint of a good ambiguity behaviour. First, the ambiguity function of the LFM-PC waveform set is derived, and the superiority of LFM-PC waveforms over LFM and PC waveforms is verified. The temporal and spatial characteristic analysis of the LFM-PC waveform set demonstrates that both the transmit beampattern and sidelobe level are mainly affected by the frequency intervals, bandwidths, and phase-coded sequences of the LFM-PC waveform set. Finally, the constrained beampattern design problem is formulated by optimizing these parameters for desired beampatterns and low sidelobes at different doppler frequencies, which is a bi-objective optimization problem. To solve this, we propose a joint optimization strategy followed by a mandatory optimization, where the sequence quadratic programming (SQP) algorithm and adaptive clonal selection (ACS) algorithm are exploited iteratively. The simulation results demonstrate the efficiency of our proposed method.<\/jats:p>","DOI":"10.3390\/s20030773","type":"journal-article","created":{"date-parts":[[2020,1,31]],"date-time":"2020-01-31T11:55:56Z","timestamp":1580471756000},"page":"773","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Constrained Transmit Beampattern Design Using a Correlated LFM-PC Waveform Set in MIMO Radar"],"prefix":"10.3390","volume":"20","author":[{"given":"Sheng","family":"Hong","sequence":"first","affiliation":[{"name":"School of Information Engineering, Nanchang University, Nanchang 330031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yantao","family":"Dong","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Nanchang University, Nanchang 330031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rui","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Ai","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Nanchang University, Nanchang 330031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuhao","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Nanchang University, Nanchang 330031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3137","DOI":"10.1109\/TSP.2010.2043976","article-title":"Phased-MIMO radar: A tradeoff between phased-array and MIMO radars","volume":"58","author":"Hassanien","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Li, J., and Stoica, P. (2008). MIMO Radar Signal Processing, Wiley-IEEE Press.","DOI":"10.1002\/9780470391488"},{"key":"ref_3","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_4","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1109\/MSP.2007.904812","article-title":"MIMO radar with colocated antenna: Review of some recent work","volume":"24","author":"Li","year":"2007","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4151","DOI":"10.1109\/TSP.2007.894398","article-title":"On probing signal design for MIMO radar","volume":"55","author":"Stoica","year":"2007","journal-title":"IEEE Trans. Signa Process."},{"key":"ref_6","unstructured":"Cheston, T.C., and Frank, J. (1990). Phased Array Radar Antennas. Radar Handbook, Horizon House Publications, Inc. [3rd ed.]."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Gini, F., Maio, A.D., and Patton, L. (2012). Waveform Design and Diversity for Advanced Radar Systems, Institution of Engineering and Technology.","DOI":"10.1049\/PBRA022E"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1558","DOI":"10.1109\/TAES.2014.140249","article-title":"Colocated MIMO radar waveform design for transmit beampattern formation","volume":"51","author":"Xu","year":"2005","journal-title":"IEEE Trans. Aerosp. Electr. Syst."},{"key":"ref_9","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_10","doi-asserted-by":"crossref","first-page":"2593","DOI":"10.1109\/TSP.2007.916139","article-title":"Waveform synthesis for diversity-based transmit beampattern design","volume":"56","author":"Stoica","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4432","DOI":"10.1109\/TSP.2012.2197615","article-title":"On the design of constant modulus probing signals for MIMO radar","volume":"60","author":"Wang","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2278","DOI":"10.1109\/TSP.2014.2310435","article-title":"MIMO radar transmit beampattern design without synthesising the covariance matrix","volume":"62","author":"Ahmed","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.sigpro.2014.03.013","article-title":"Single-stage transmit beamforming design for MIMO radar","volume":"102","author":"Soltanalian","year":"2014","journal-title":"Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2049","DOI":"10.1109\/TSP.2015.2398841","article-title":"MIMO radar transmit beampattern matching design","volume":"63","author":"Zhang","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","first-page":"543","article-title":"Waveform optimization for transmit beamforming with MIMO radar antenna arrays","volume":"63","author":"Guo","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1421","DOI":"10.1109\/TAES.2016.140023","article-title":"MIMO radar waveform design for transmit beamforming and orthogonality","volume":"52","author":"Deng","year":"2016","journal-title":"IEEE Trans. Aerosp. Electr. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2669","DOI":"10.1109\/TSP.2011.2125960","article-title":"Transmit energy focusing for DOA estimation in MIMO radar with colocated antennas","volume":"59","author":"Hassanien","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3376","DOI":"10.1109\/TAES.2012.6324717","article-title":"On transmit beamforming for MIMO radar","volume":"48","author":"Friedlander","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2963","DOI":"10.1109\/TSP.2013.2252173","article-title":"MIMO radar transmit beampattern design with ripple and transition band control","volume":"61","author":"Hua","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Aittomaki, T., and Koivunen, V. (November, January 29). MIMO Radar Beampattern Optimization with Ripple Control Using Sum-of-Squares Representation. Proceedings of the 2017 51st Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA.","DOI":"10.1109\/ACSSC.2017.8335407"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1049\/el.2017.0167","article-title":"Robust transmit beampattern matching synthesis for MIMO radar","volume":"53","author":"Cheng","year":"2017","journal-title":"Eectron. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Aldayel, O., Monga, V., and Rangaswamy, M. (2017, January 8\u201312). Transmit MIMO Beampattern Design under Constant Modulus and Spectral Interference Constraints. Proceedings of the 2017 IEEE Radar Conference (RadarConf), Seattle, WA, USA.","DOI":"10.1109\/RADAR.2017.7944374"},{"key":"ref_23","first-page":"136","article-title":"MIMO radar waveform design method based on quadratically spatial and spectral optimizations under jamming","volume":"39","author":"Wang","year":"2017","journal-title":"J. Natl. Univ. Def. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1109\/LSP.2017.2663406","article-title":"SINR enhancement in colocated MIMO radar using transmit covariance matrix optimization","volume":"24","author":"Haghnegahdar","year":"2017","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Cheng, Z., Liao, B., He, Z., and Li, Y. (2018, January 19\u201321). Spectrally Compatible Waveform Design for MIMO Radar with Transmit Beampattern Formation. Proceedings of the 2018 IEEE 23rd International Conference on Digital Signal Processing (DSP), Shanghai, China.","DOI":"10.1109\/ICDSP.2018.8631692"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"ZHAI, Q., WANG, Y., and Wei, L.I. (2016, January 16\u201318). MIMO Radar Transmit Beampattern Design with PAR Constraint in a Spectrally Crowded Environment. Proceedings of the International Conference on Computer Networks and Communication Technology (CNCT 2016), Xiamen, China.","DOI":"10.2991\/cnct-16.2017.51"},{"key":"ref_27","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_28","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.sigpro.2017.10.010","article-title":"Constrained transmit beampattern design for colocated MIMO radar","volume":"144","author":"Yu","year":"2018","journal-title":"Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1615","DOI":"10.1109\/TGRS.2014.2346478","article-title":"MIMO SAR OFDM chirp waveform diversity design with random matrix modulation","volume":"53","author":"Wang","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5926","DOI":"10.1109\/TSP.2008.929658","article-title":"MIMO radar ambiguity properties and optimization using frequency-hopping waveforms","volume":"56","author":"Chen","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Hua, G., and Abeysekera, S.S. (2015, January 19\u201324). Robust Transmit Beampattern Design for Uniform Linear Arrays Using Correlated LFM Waveforms. Proceedings of the 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brisbane, QLD, Australia.","DOI":"10.1109\/ICASSP.2015.7178422"},{"key":"ref_32","first-page":"927","article-title":"MIMO radar waveform design for OFD-LFM with various frequency steps","volume":"38","author":"Li","year":"2016","journal-title":"J. Electron. Inf. Technol."},{"key":"ref_33","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 optimized pulse compression property of spatial synthesized signals","volume":"10","author":"Li","year":"2016","journal-title":"IET Radar Sonar Navig."},{"key":"ref_34","first-page":"1","article-title":"Design and characteristic analysis of hybrid OFD-LFM-PC waveforms in the MIMO radar","volume":"2019","author":"Hong","year":"2019","journal-title":"J. Eng."},{"key":"ref_35","unstructured":"Rau, N.S. (2003). Optimization Principles: Practical Applications to the Operation and Markets of the Electric Power Industry, Wiley-IEEE Press."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2769","DOI":"10.1007\/s12206-016-0538-2","article-title":"Fractional-order control of active suspension actuator based on parallel adaptive clonal selection algorithm","volume":"30","author":"Dong","year":"2016","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_37","first-page":"425","article-title":"Inter-pulse pseudo-random binary-phase code and linear frequency modulation combined detecting system","volume":"28","author":"Xiong","year":"2007","journal-title":"Acta Armamentarii"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1049\/el.2015.1637","article-title":"Convex optimisation based transmit beampattern synthesis for MIMO radar","volume":"52","author":"Pandey","year":"2016","journal-title":"Electron. Lett."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/j.sigpro.2013.06.021","article-title":"Transmit beampattern design based on convex optimization for MIMO radar systems","volume":"94","author":"Gong","year":"2014","journal-title":"Signal Process."},{"key":"ref_40","unstructured":"Grant, M., and Boyd, S. (2020, January 31). CVX: Matlab Software for Disciplined Convex Programming, Version 2.1. Available online: http:\/\/cvxr.com\/cvx\/."},{"key":"ref_41","unstructured":"Lin, C., and Dong, J. (1992). Method and Theory of Multi-objective Optimization, Jilin Education Press."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Alaee-Kerahroodi, M., Mishra, K.V., Shankar, M.R.B., and Ottersten, B. (2019, January 2\u20135). Discrete-phase sequence design for coexistence of MIMO radar and MIMO communications. Proceedings of the 2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Cannes, France.","DOI":"10.1109\/SPAWC.2019.8815508"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Gill, P.E., and Wong, E. (2012). Sequential Quadratic Programming Methods, Springer.","DOI":"10.1007\/978-1-4614-1927-3_6"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/3\/773\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:53:25Z","timestamp":1760172805000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/3\/773"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,31]]},"references-count":43,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["s20030773"],"URL":"https:\/\/doi.org\/10.3390\/s20030773","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,1,31]]}}}