{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T18:39:59Z","timestamp":1761676799800,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T00:00:00Z","timestamp":1572307200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we propose a novel direction-of-arrival (DOA) estimation structure based on multiple-input multiple-output (MIMO) radar with colocated antennas, referred to as compressive measurement-based MIMO (CM-MIMO) radar, where the compressive sensing (CS) is employed to reduce the number of channels. Therefore, the system complexity and the computational burden are effectively reduced. It is noted that CS is used after the matched filters and that a measurement matrix with less rows than columns is multiplied with the received signals. As a result, the configurations of the transmit and receive antenna arrays are not affected by the CS and can be determined according to the practical requirements. To study the estimation performance, the Cram\u00e9r\u2013Rao bound (CRB) with respect to the DOAs of the proposed CM-MIMO radar is analyzed in this paper. The derived CRB expression is also suitable for the conventional MIMO radar by setting the measurement matrix as an identity matrix. Moreover, the CRB expression can work in the under-determined case, since the sum-difference coarray structure is considered. However, the random measurement matrix leads to high information loss, thus compromising the estimation performance. To overcome this problem, we consider that the a prior probability distribution of the DOAs associated with the targets can be obtained in many scenarios and an optimization approach for the measurement matrix is proposed in this paper, where the maximum mutual information criterion is adopted. The superiority of the proposed structure is validated by numerical simulations.<\/jats:p>","DOI":"10.3390\/s19214706","type":"journal-article","created":{"date-parts":[[2019,10,31]],"date-time":"2019-10-31T05:18:26Z","timestamp":1572499106000},"page":"4706","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["A MIMO Radar-Based DOA Estimation Structure Using Compressive Measurements"],"prefix":"10.3390","volume":"19","author":[{"given":"Tao","family":"Chen","sequence":"first","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"},{"name":"Beijing Institute of Remote Sensing Equipment, Beijing 100854, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7013-9612","authenticated-orcid":false,"given":"Muran","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Van Trees, H.L. (2002). Detection, Estimation, and Modulation Theory, Part IV: Optimum Array Processing, Wiley.","DOI":"10.1002\/0471221104"},{"key":"ref_2","unstructured":"Chandran, S. (2006). Advances in Direction-of-Arrival Estimation, Artech House."},{"key":"ref_3","unstructured":"Forsythe, K.W., Bliss, D.W., and Fawcett, G.S. (2004, January 7\u201310). Multiple-input multiple-output (MIMO) radar: Performance issues. Proceedings of the 38th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA."},{"key":"ref_4","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_5","unstructured":"Fishler, E., Haimovich, A., Blum, R., Chizhik, D., Cimini, L., and Valenzuela, R. (2004, January 29). MIMO radar: An idea whose time has come. Proceedings of the IEEE Radar Conference, Philadelphia, PA, USA."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Li, J., and Stoica, J. (2009). MIMO Radar Signal Processing, Wiley.","DOI":"10.1002\/9780470391488"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3590","DOI":"10.1109\/TWC.2010.092810.091092","article-title":"Noncooperative cellular wireless with unlimited numbers of BS antennas","volume":"9","author":"Marzetta","year":"2010","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Fortunati, S., Sanguinetti, L., Greco, M.S., and Gini, F. (2019, January 12\u201317). Scaling up MIMO radar for target detection. Proceedings of the IEEE ICASSP, Brighton, UK.","DOI":"10.1109\/ICASSP.2019.8683870"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","article-title":"Compressed sensing","volume":"52","author":"Donoho","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/MSP.2007.914731","article-title":"An introduction to compressive sampling","volume":"25","author":"Wakin","year":"2008","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_11","first-page":"509","article-title":"Sparse methods for direction-of-arrival estimation","volume":"Volume 7","author":"Chellappa","year":"2018","journal-title":"Academic Press Library in Signal Processing"},{"key":"ref_12","first-page":"21","article-title":"Source estimation using coprime array: A Sparse Reconstruction Perspective","volume":"25","author":"Shi","year":"2008","journal-title":"IEEE Sens. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1710","DOI":"10.1109\/LSP.2018.2872400","article-title":"Off-grid direction-of-arrival estimation using coprime array interpolation","volume":"25","author":"Zhou","year":"2018","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"5956","DOI":"10.1109\/TSP.2018.2872012","article-title":"Direction-of-arrival estimation for coprime array via virtual array interpolation","volume":"66","author":"Zhou","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1754","DOI":"10.1109\/TAES.2011.5937263","article-title":"Spatial compressive sensing for direction-of-arrival estimation of multiple sources using dynamic sensor arrays","volume":"47","author":"Bilik","year":"2011","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3828","DOI":"10.1109\/TAP.2013.2256093","article-title":"Directions-of-arrival estimation through Bayesian Compressive Sensing strategies","volume":"61","author":"Carlin","year":"2013","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3203","DOI":"10.1109\/TAP.2017.2684137","article-title":"Single-snapshot DoA estimation in array antennas with mutual coupling through a multi-scaling BCS strategy","volume":"65","author":"Rocca","year":"2017","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_18","unstructured":"Chen, C.Y., and Vaidyanathan, P.P. (2008, January 26\u201329). Compressed sensing in MIMO radar. Proceedings of the 2008 42nd Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Petropulu, A.P., Yu, Y., and Poor, H.V. (2008, January 26\u201329). Distributed MIMO radar using compressive sampling. Proceedings of the 2008 42nd Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA.","DOI":"10.1109\/ACSSC.2008.5074392"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1109\/JSTSP.2009.2038973","article-title":"MIMO radar using compressive sampling","volume":"4","author":"Yu","year":"2010","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5338","DOI":"10.1109\/TSP.2011.2162328","article-title":"Measurement matrix design for compressive sensing\u2013based MIMO radar","volume":"59","author":"Yu","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1490","DOI":"10.1109\/TAES.2012.6178074","article-title":"CSSF MIMO radar: Compressive-sensing and step-frequency based MIMO radar","volume":"48","author":"Yu","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1109\/TSP.2013.2289875","article-title":"Spatial compressive sensing for MIMO radar","volume":"62","author":"Rossi","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Alawsh, S.A., Muqaibel, A.H., and Sharawi, M.S. (2015, January 3\u20135). DOA estimation in MIMO systems with compressive sensing for future handsets. Proceedings of the 2015 IEEE Jordan Conference on Applied Electrical Engineering and Computing Technologies (AEECT), Amman, Jordan.","DOI":"10.1109\/AEECT.2015.7360532"},{"key":"ref_25","unstructured":"Wang, Y., Leus, G., and Pandharipande, A. (September, January 31). Direction estimation using compressive sampling array processing. Proceedings of the IEEE Statistical Signal Processing Workshop, Cardiff, UK."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Gu, J.F., Zhu, W.P., and Swamy, M.N.S. (2011, January 15\u201318). Compressed sensing for DOA estimation with fewer receivers than sensors. Proceedings of the IEEE International Symposium on Circuits and Systems, Rio de Janeiro, Brazil.","DOI":"10.1109\/ISCAS.2011.5937922"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"6423","DOI":"10.1109\/TSP.2015.2464183","article-title":"Analysis of Fisher information and the Cram\u00e9r-Rao bound for nonlinear parameter estimation after random compression","volume":"63","author":"Pakrooh","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.sigpro.2017.03.013","article-title":"Design and analysis of compressive antenna arrays for direction of arrival estimation","volume":"138","author":"Ibrahim","year":"2017","journal-title":"Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Gu, Y., Zhang, Y.D., and Goodman, N.A. (2017, January 5\u20139). Optimized compressive sensing-based direction-of-arrival estimation in massive MIMO. Proceedings of the IEEE ICASSP, New Orleans, LA, USA.","DOI":"10.1109\/ICASSP.2017.7952743"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4525","DOI":"10.1109\/TSP.2017.2706187","article-title":"Information-theoretic compressive sensing kernel optimization and Bayesian Cram\u00e9r-Rao bound for time delay estimation","volume":"65","author":"Gu","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1719","DOI":"10.1049\/iet-com.2016.1048","article-title":"Compressive sensing based coprime array direction-of-arrival estimation","volume":"11","author":"Zhou","year":"2017","journal-title":"IET Commun."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"4133","DOI":"10.1109\/TSP.2018.2847645","article-title":"DOA estimation using compressed sparse array","volume":"66","author":"Guo","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1438","DOI":"10.1109\/LSP.2015.2409153","article-title":"Remarks on the spatial smoothing step in coarray MUSIC","volume":"22","author":"Liu","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Ahmed, A., Zhang, Y.D., and Himed, B. (2017, January 8\u201312). Effective nested array design for fourth-order cumulant-based DOA estimation. Proceedings of the IEEE Radar Conference, Seattle, WA, USA.","DOI":"10.1109\/RADAR.2017.7944349"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1109\/TIT.2011.2171529","article-title":"Compressive MUSIC: Revisiting the link between compressive sensing and array signal processing","volume":"58","author":"Kim","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1600","DOI":"10.1109\/TAP.2005.846723","article-title":"Time reversal imaging of obscured targets from multistatic data","volume":"53","author":"Devaney","year":"2005","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2650","DOI":"10.1109\/TSP.2015.2417507","article-title":"Performance analysis of time-reversal MUSIC","volume":"63","author":"Ciuonzo","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1109\/LSP.2017.2661246","article-title":"Noncolocated time-reversal MUSIC: High-SNR distribution of null spectrum","volume":"24","author":"Ciuonzo","year":"2017","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1024","DOI":"10.1109\/LSP.2017.2704612","article-title":"On time-reversal imaging by statistical testing","volume":"24","author":"Ciuonzo","year":"2017","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/0005-1098(78)90005-5","article-title":"Modeling by shortest data description","volume":"14","author":"Rissanen","year":"1978","journal-title":"Automatica"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1109\/LCOMM.2016.2618789","article-title":"DOA estimation based on combined unitary ESPRIT for coprime MIMO radar","volume":"21","author":"Li","year":"2017","journal-title":"IEEE Commun. Lett."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1628","DOI":"10.1109\/LSP.2015.2417807","article-title":"Sparsity-based direction finding of coherent and uncorrelated targets using active nonuniform arrays","volume":"22","author":"BouDaher","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.dsp.2016.06.006","article-title":"DOA estimation of mixed coherent and uncorrelated targets exploiting coprime MIMO radar","volume":"61","author":"Qin","year":"2017","journal-title":"Digit. Signal Process."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1109\/97.917699","article-title":"The stochastic CRB for array processing: A textbook derivation","volume":"8","author":"Stoica","year":"2001","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_45","unstructured":"Golub, G.H., and van Loan, C.F. (1996). Matrix Computations, Johns Hopkins University Press. [3rd ed.]."},{"key":"ref_46","unstructured":"Magnus, J.R., and Neudecker, J.R. (1999). Matrix Differential Calculus with Applications in Statistics and Econometrics, Wiley."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"3194","DOI":"10.1109\/TSP.2014.2323022","article-title":"Radar target profiling and recognition based on TSI-optimized compressive sensing kernel","volume":"62","author":"Gu","year":"2014","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/21\/4706\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:30:21Z","timestamp":1760189421000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/21\/4706"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,29]]},"references-count":47,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2019,11]]}},"alternative-id":["s19214706"],"URL":"https:\/\/doi.org\/10.3390\/s19214706","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,10,29]]}}}