{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T23:22:52Z","timestamp":1768432972708,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2023,11,3]],"date-time":"2023-11-03T00:00:00Z","timestamp":1698969600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Project of Scientific and Technological Innovation Development of Jilin","award":["20210103090"],"award-info":[{"award-number":["20210103090"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Realization and enhancement of detection techniques for multiple-input\u2013multiple-output (MIMO) radar systems require polyphase code sequences with excellent orthogonality characteristics. Therefore, orthogonal waveform design is the key to realizing MIMO radar. Conventional orthogonal waveform design methods fail to ensure acceptable orthogonal characteristics by individually optimizing the autocorrelation sidelobe peak level and the cross-correlation sidelobe peak level. In this basis, the multi-objective Archimedes optimization algorithm (MOIAOA) is proposed for orthogonal waveform optimization while simultaneously minimizing the total autocorrelation sidelobe peak energy and total cross-correlation peak energy. A novel optimal individual selection method is proposed to select those individuals that best match the weight vectors and lead the evolution of these individuals to their respective neighborhoods. Then, new exploration and development phases are introduced to improve the algorithm\u2019s ability to increase its convergence speed and accuracy. Subsequently, novel incentive functions are formulated based on distinct evolutionary phases, followed by the introduction of a novel environmental selection method aimed at comprehensively enhancing the algorithm\u2019s convergence and distribution. Finally, a weight updating method based on the shape of the frontier surface is proposed to dynamically correct the shape of the overall frontier, further enhancing the overall distribution. The results of experiments on the orthogonal waveform design show that the multi-objective improved Archimedes optimization algorithm (MOIAOA) achieves superior orthogonality, yielding lower total autocorrelation sidelobe peak energy and total cross-correlation peak energy than three established methods.<\/jats:p>","DOI":"10.3390\/rs15215231","type":"journal-article","created":{"date-parts":[[2023,11,3]],"date-time":"2023-11-03T10:59:54Z","timestamp":1699009194000},"page":"5231","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Novel MIMO Radar Orthogonal Waveform Design Algorithm Based on the Multi-Objective Improved Archimedes Optimization Algorithm"],"prefix":"10.3390","volume":"15","author":[{"given":"Yanjiao","family":"Wang","sequence":"first","affiliation":[{"name":"School of Electrical Engineering, Northeast Electric Power University, 169 Changchun Road, Jilin 132012, China"}]},{"given":"Mingchi","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Northeast Electric Power University, 169 Changchun Road, Jilin 132012, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wen, F., Ren, D., and Zhang, X. (2023). Fast Localizing for Anonymous UAVs Oriented Toward Polarized Massive MIMO Systems. IEEE Internet Things J., 1.","DOI":"10.1109\/JIOT.2023.3282644"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1109\/LSP.2023.3296038","article-title":"2D-DOA estimation for coherent signals via a polarized uniform rectangular array","volume":"30","author":"Zhang","year":"2023","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Wang, X., Guo, Y., Wen, F., He, J., and Truong, K.T. (2023). EMVS-MIMO radar with sparse Rx geometry: Tensor modeling and 2D direction finding. IEEE Trans. Aerosp. Electron. Syst., 1\u201314.","DOI":"10.1109\/TAES.2023.3297570"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3071","DOI":"10.1109\/TWC.2022.3215965","article-title":"Compressive sampling framework for 2D-DOA and polarization estimation in mmWave polarized massive MIMO systems","volume":"22","author":"Wen","year":"2023","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1109\/TAES.2007.4383581","article-title":"Design principles of MIMO radar detectors","volume":"43","author":"Lops","year":"2007","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6195","DOI":"10.1109\/TSP.2010.2072923","article-title":"Space-time coding for MIMO radar detection and ranging","volume":"58","author":"Jajamovich","year":"2010","journal-title":"IEEE Trans. Signal Process"},{"key":"ref_7","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. Electron. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1016\/j.sigpro.2009.07.033","article-title":"Optimal and robust waveform design for MIMO radars in the presence of clutter","volume":"90","author":"Naghibi","year":"2010","journal-title":"Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Zhang, L., Wang, H., Wen, F.N., and Shi, J.P. (2022). PARAFAC estimators for coherent targets in EMVS-MIMO radar with arbitrary geometry. Remote Sens., 14.","DOI":"10.3390\/rs14122905"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Wang, J.H., Fan, P.Z., Yang, Y., and Guan, Y.L. (2019, January 8\u201311). Range\/Doppler Sidelobe Suppression in Moving Target Detection Based on Time-Frequency Binomial Design. Proceedings of the 2019 IEEE 30th Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), Istanbul, Turkey.","DOI":"10.1109\/PIMRC.2019.8904374"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zhu, J.H., Song, Y.P., Jiang, N., Xie, Z., Fan, C.Y., and Huang, X.T. (2023). Enhanced Doppler Resolution and Sidelobe Suppression Performance for Golay Complementary Waveforms. Remote Sens., 15.","DOI":"10.3390\/rs15092452"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4391","DOI":"10.1109\/TSP.2009.2025108","article-title":"Designing unimodular sequence sets with good correlations\u2014Including an application to MIMO radar","volume":"57","author":"He","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2866","DOI":"10.1109\/TSP.2016.2535312","article-title":"Sequence set design with good correlation properties via majorization-minimization","volume":"64","author":"Song","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.1109\/TSP.2017.2787104","article-title":"Fast algorithms for designing unimodular waveform(s) with good correlation properties","volume":"66","author":"Li","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","unstructured":"Wang, X., Liu, H., Yan, J., Hu, L., and Bao, Z. (2011, January 24\u201327). Waveform design with low sidelobe and low correlation properties for MIMO radar. Proceedings of the 2011 IEEE CIE International Conference on Radar, Chengdu, China."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1109\/LSP.2006.877143","article-title":"Optimizing polyphase sequences for orthogonal netted radar","volume":"13","author":"Khan","year":"2006","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3126","DOI":"10.1109\/TSP.2004.836530","article-title":"Polyphase code design for orthogonal netted radar systems","volume":"52","author":"Deng","year":"2004","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1953","DOI":"10.1109\/TAES.2016.140671","article-title":"Design of OFDM radar pulses using genetic algorithm based techniques","volume":"52","author":"Lellouch","year":"2016","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhang, L., and Wen, F.Q. (2021). A novel MIMO radar orthogonal waveform design algorithm based on intelligent ions motion. Remote Sens., 13.","DOI":"10.3390\/rs13101968"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"13561","DOI":"10.1109\/ACCESS.2019.2893970","article-title":"Greedy Code Search Based Memetic Algorithm for the Design of Orthogonal Polyphase Code Sets","volume":"7","author":"Ren","year":"2019","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Liu, B., He, Z.S., Zeng, J.K., and Liu, B.Y. (2006). Polyphase orthogonal code design for MIMO radar systems. Proc. Int. Conf. Radar., 1\u20134.","DOI":"10.1109\/ICR.2006.343409"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"381","DOI":"10.3969\/j.issn.1004-4132.2011.03.003","article-title":"Polyphase coded signal design for MIMO radar using MO-MicPSO","volume":"22","author":"Zeng","year":"2011","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Li, Y.R., and Hu, H.Y. (2015, January 24\u201325). Orthogonal poly-phase code design based on adaptive mix algorithm in MIMO radar. Proceedings of the 2015 International Conference on Automation, Mechanical Control and Computational Engineering, Changsha, China.","DOI":"10.2991\/amcce-15.2015.237"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Stringer, J., Lamont, G., and Akers, G. (2012, January 10\u201315). Radar phase-coded waveform design using MOEAs. Proceedings of the 2012 IEEE Congress on Evolutionary Computation, Brisbane, Australia.","DOI":"10.1109\/CEC.2012.6256554"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1531","DOI":"10.1007\/s10489-020-01893-z","article-title":"Archimedes optimization algorithm: A new metaheuristic algorithm for solving optimization problems","volume":"51","author":"Hashim","year":"2021","journal-title":"Appl. Intell."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1109\/TEVC.2007.892759","article-title":"MOEA\/D: A multi-objective evolutionary algorithm based on decomposition","volume":"11","author":"Zhang","year":"2007","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_27","first-page":"577","article-title":"An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints","volume":"66","author":"Deb","year":"2018","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1109\/TEVC.2008.925798","article-title":"Multi-objective optimization problems with complicated Pareto sets, MOEA\/D and NSGA-II","volume":"13","author":"Li","year":"2009","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1016\/j.ins.2015.07.018","article-title":"A new multi-objective particle swarm optimization algorithm based on decomposition","volume":"325","author":"Dai","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1109\/TEVC.2016.2587808","article-title":"A vector angle-based evolutionary algorithm for unconstrained many-objective optimization","volume":"21","author":"Xiang","year":"2017","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1109\/TEVC.2005.861417","article-title":"A review of multiobjective test problems and a scalable test problem toolkit","volume":"10","author":"Huband","year":"2006","journal-title":"IEEE Trans. Evol. Comput."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/21\/5231\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:16:41Z","timestamp":1760131001000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/21\/5231"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,3]]},"references-count":31,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["rs15215231"],"URL":"https:\/\/doi.org\/10.3390\/rs15215231","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,3]]}}}