{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,26]],"date-time":"2026-04-26T06:02:49Z","timestamp":1777183369853,"version":"3.51.4"},"reference-count":41,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2017,8,3]],"date-time":"2017-08-03T00:00:00Z","timestamp":1501718400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["No. LR16F010002"],"award-info":[{"award-number":["No. LR16F010002"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. U1401253"],"award-info":[{"award-number":["No. U1401253"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Fundamental Research Funds for the Central Universities","award":["No. 2017XZZX009-01"],"award-info":[{"award-number":["No. 2017XZZX009-01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A coprime array is capable of achieving more degrees-of-freedom for direction-of-arrival (DOA) estimation than a uniform linear array when utilizing the same number of sensors. However, existing algorithms exploiting coprime array usually adopt predefined spatial sampling grids for optimization problem design or include spectrum peak search process for DOA estimation, resulting in the contradiction between estimation performance and computational complexity. To address this problem, we introduce the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) to the coprime coarray domain, and propose a novel coarray ESPRIT-based DOA estimation algorithm to efficiently retrieve the off-grid DOAs. Specifically, the coprime coarray statistics are derived according to the received signals from a coprime array to ensure the degrees-of-freedom (DOF) superiority, where a pair of shift invariant uniform linear subarrays is extracted. The rotational invariance of the signal subspaces corresponding to the underlying subarrays is then investigated based on the coprime coarray covariance matrix, and the incorporation of ESPRIT in the coarray domain makes it feasible to formulate the closed-form solution for DOA estimation. Theoretical analyses and simulation results verify the efficiency and the effectiveness of the proposed DOA estimation algorithm.<\/jats:p>","DOI":"10.3390\/s17081779","type":"journal-article","created":{"date-parts":[[2017,8,3]],"date-time":"2017-08-03T09:47:19Z","timestamp":1501753639000},"page":"1779","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":86,"title":["Direction-of-Arrival Estimation with Coarray ESPRIT for Coprime Array"],"prefix":"10.3390","volume":"17","author":[{"given":"Chengwei","family":"Zhou","sequence":"first","affiliation":[{"name":"College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinfang","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,8,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Van Trees, H.L. (2002). Detection, Estimation, and Modulation Theory, Wiley. Part IV: Optimum Array Processing.","DOI":"10.1002\/0471221104"},{"key":"ref_2","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_3","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 42nd IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, LA, USA.","DOI":"10.1109\/ICASSP.2017.7952743"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4916","DOI":"10.1109\/JSEN.2017.2709329","article-title":"A fast gridless covariance matrix reconstruction method for one-and two-dimensional direction-of-arrival estimation","volume":"17","author":"Wu","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_5","first-page":"1","article-title":"Asynchronous broadcast-based decentralized learning in sensor networks","volume":"32","author":"Zhao","year":"2017","journal-title":"Int. J. Parallel Emerg. Distrib. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2527","DOI":"10.1109\/JSEN.2016.2517128","article-title":"Efficient two-dimensional direction-of-arrival estimation for a mixture of circular and noncircular sources","volume":"16","author":"Chen","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3911","DOI":"10.1002\/sec.1543","article-title":"Secured measurement fusion scheme against deceptive ECM attack in radar network","volume":"9","author":"Yang","year":"2016","journal-title":"Secur. Commun. Netw."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1109\/LAWP.2014.2360419","article-title":"Improved azimuth\/elevation angle estimation algorithm for three-parallel uniform linear arrays","volume":"14","author":"Chen","year":"2015","journal-title":"IEEE Antennas Wireless Propag. Lett."},{"key":"ref_9","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."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3881","DOI":"10.1109\/TSP.2012.2194289","article-title":"Robust adaptive beamforming based on interference covariance matrix reconstruction and steering vector estimation","volume":"60","author":"Gu","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Yang, C., Zhang, H., Qu, F., and Shi, Z. (2015, January 12\u201315). Performance of target tracking in radar network system under deception attack. Proceedings of the 10th International Conference on Wireless Algorithms, Systems, and Applications (WASA 2015), Qufu, China.","DOI":"10.1007\/978-3-319-21837-3_65"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wang, B., Wang, W., Gu, Y., and Lei, S. (2017). Underdetermined DOA estimation of quasi-stationary signals using a partly-calibrated array. Sensors, 17.","DOI":"10.3390\/s17040702"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Wu, X., Zhu, W.P., and Yan, J. (2017). A Toeplitz covariance matrix reconstruction approach for direction-of-arrival estimation. IEEE Trans. Veh. Technol.","DOI":"10.1109\/ICASSP.2017.7952740"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.sigpro.2017.05.024","article-title":"ESPRIT-like two-dimensional direction finding for mixed circular and strictly noncircular sources based on joint diagonalization","volume":"141","author":"Chen","year":"2017","journal-title":"Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/j.sigpro.2013.10.009","article-title":"Robust adaptive beamforming based on interference covariance matrix sparse reconstruction","volume":"96","author":"Gu","year":"2014","journal-title":"Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2824","DOI":"10.1109\/JSEN.2014.2316798","article-title":"Cumulants-based Toeplitz matrices reconstruction method for 2-D coherent DOA estimation","volume":"14","author":"Chen","year":"2014","journal-title":"IEEE Sens. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2004","DOI":"10.1109\/JSEN.2015.2508059","article-title":"Direction of arrival estimation for off-grid signals based on sparse Bayesian learning","volume":"16","author":"Wu","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1109\/MWC.2016.7422408","article-title":"5 G Ultra-dense cellular networks","volume":"23","author":"Ge","year":"2016","journal-title":"IEEE Wirel. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1109\/TSP.2010.2089682","article-title":"Sparse sensing with co-prime samplers and arrays","volume":"59","author":"Vaidyanathan","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1109\/TAP.1968.1139138","article-title":"Minimum-redundancy linear arrays","volume":"16","author":"Moffet","year":"1968","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1109\/PROC.1977.10517","article-title":"Applications of numbered undirected graphs","volume":"65","author":"Bloom","year":"1977","journal-title":"Proc. IEEE"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Zhou, C., Gu, Y., Zhang, Y.D., Shi, Z., Jin, T., and Wu, X. (2017). Compressive sensing based coprime array direction-of-arrival estimation. IET Commun.","DOI":"10.1049\/iet-com.2016.1048"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1109\/TSP.2015.2393838","article-title":"Generalized coprime array configurations for direction-of-arrival estimation","volume":"63","author":"Qin","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Shen, Y., Zhou, C., Gu, Y., Lin, H., and Shi, Z. (2017, January 3\u20136). Vandermonde decomposition of coprime coarray covariance matrix for DOA estimation. Proceedings of the 18th IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Sapporo, Japan.","DOI":"10.1109\/SPAWC.2017.8227643"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zhou, C., Gu, Y., He, S., and Shi, Z. (2017). A robust and efficient algorithm for coprime array adaptive beamforming. IEEE Trans. Veh. Technol.","DOI":"10.1109\/TVT.2017.2704610"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhou, C., Shi, Z., and Gu, Y. (2017, January 8\u201312). Coprime array adaptive beamforming with enhanced degrees-of-freedom capability. Proceedings of the 2017 IEEE Radar Conference (RadarConf17), Seattle, WA, USA.","DOI":"10.1109\/RADAR.2017.7944417"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Gu, Y., Zhou, C., Goodman, N.A., Song, W.Z., and Shi, Z. (2016, January 20\u201325). Coprime array adaptive beamforming based on compressive sensing virtual array signal. Proceedings of the 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, China.","DOI":"10.1109\/ICASSP.2016.7472224"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Zhou, C., Gu, Y., Song, W.Z., Xie, Y., and Shi, Z. (2016, January 20\u201325). Robust adaptive beamforming based on DOA support using decomposed coprime subarrays. Proceedings of the 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, China.","DOI":"10.1109\/ICASSP.2016.7472225"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1109\/TSP.2016.2614799","article-title":"Generalized coprime sampling of Toeplitz matrices for spectrum estimation","volume":"65","author":"Qin","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zhou, C., Shi, Z., Gu, Y., and Goodman, N.A. (2015, January 19\u201324). DOA estimation by covariance matrix sparse reconstruction of coprime array. Proceedings of the 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brisbane, Australia.","DOI":"10.1109\/ICASSP.2015.7178395"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1109\/TAP.1986.1143830","article-title":"Multiple emitter location and signal parameter estimation","volume":"34","author":"Schmidt","year":"1986","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Pal, P., and Vaidyanathan, P.P. (2011, January 4\u20137). Coprime sampling and the MUSIC algorithm. Proceedings of the IEEE Signal Processing Society 14th DSPWorkshop & 6th SPEWorkshop, Sedona, AZ, USA.","DOI":"10.1109\/DSP-SPE.2011.5739227"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Wu, X., Zhu, W.P., Yan, J., and Zhang, Z. (2017). Two sparse-based methods for off-grid direction-of-arrival estimation. Signal Process.","DOI":"10.1016\/j.sigpro.2017.07.004"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Zhang, Y.D., Amin, M.G., and Himed, B. (2013, January 26\u201331). Sparsity-based DOA estimation using co-prime arrays. Proceedings of the 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vancouver, Canada.","DOI":"10.1109\/ICASSP.2013.6638403"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1109\/JSEN.2016.2637059","article-title":"Source estimation using coprime array: A sparse reconstruction perspective","volume":"17","author":"Shi","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Liu, C.L., Vaidyanathan, P.P., and Pal, P. (2016, January 22\u201325). Coprime coarray interpolation for DOA estimation via nuclear norm minimization. Proceedings of the 2016 IEEE International Symposium on Circuits and Systems (ISCAS), Montr\u00e9al, QC, Canada.","DOI":"10.1109\/ISCAS.2016.7539135"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Fan, X., Zhou, C., Gu, Y., and Shi, Z. (2017, January 4\u20137). Toeplitz matrix reconstruction of interpolated coprime virtual array for DOA estimation. Proceedings of the IEEE 85th Vehicular Technology Conference: VTC2017-Spring, Sydney, Australia.","DOI":"10.1109\/VTCSpring.2017.8108559"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Sun, F., Gao, B., Chen, L., and Lan, P. (2016). A low-complexity ESPRIT-based DOA estimation method for co-prime linear arrays. Sensors, 16.","DOI":"10.3390\/s16091367"},{"key":"ref_39","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_40","unstructured":"Zhou, C., Shi, Z., Gu, Y., and Shen, X. (2013, January 24\u201326). DECOM: DOA estimation with combined MUSIC for coprime array. Proceedings of the 2013 International Conference on Wireless Communications and Signal Processing (WCSP), Hangzhou, China."},{"key":"ref_41","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."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/8\/1779\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:45:09Z","timestamp":1760208309000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/8\/1779"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,3]]},"references-count":41,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2017,8]]}},"alternative-id":["s17081779"],"URL":"https:\/\/doi.org\/10.3390\/s17081779","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8,3]]}}}