{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:31:45Z","timestamp":1760239905884,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,1,15]],"date-time":"2019-01-15T00:00:00Z","timestamp":1547510400000},"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>A two-stage method is proposed to jointly estimate the direction-of-arrival (DOA) and carrier frequency (CF) of multiple sources, by using two orthogonal coprime arrays (CPAs). The DOAs of CF-known sources are estimated first by applying a spatial smoothing MUSIC algorithm. The contribution of these source signals is then removed from the originally received signal by applying an orthogonal complement projector. Next, a joint-ESPRIT algorithm is applied to estimate the DOAs and CFs of the remaining CF-unknown sources. With two orthogonal CPA(5, 6), the RMSE of DOA and CF of applying the proposed method to 30 sources, 13 of which have unknown CF, is less than 1% at SNR     &gt; 5     dB.<\/jats:p>","DOI":"10.3390\/s19020335","type":"journal-article","created":{"date-parts":[[2019,1,16]],"date-time":"2019-01-16T03:09:13Z","timestamp":1547608153000},"page":"335","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Joint Estimation of DOA and Frequency of Multiple Sources with Orthogonal Coprime Arrays"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3261-7510","authenticated-orcid":false,"given":"Kai-Chieh","family":"Hsu","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, National Taiwan University, Taipei 106, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9944-3431","authenticated-orcid":false,"given":"Jean-Fu","family":"Kiang","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, National Taiwan University, Taipei 106, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,15]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"984","DOI":"10.1109\/29.32276","article-title":"ESPRIT-estimation of signal parameters via rotational invariance techniques","volume":"37","author":"Roy","year":"1989","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_3","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_4","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_5","doi-asserted-by":"crossref","unstructured":"Haardt, M., and Nossek, J.A. (1997). 3-D unitary ESPRIT for joint angle and carrier estimation. IEEE Int. Conf. Acoust. Speech Signal Process., 255\u2013258.","DOI":"10.1109\/ICASSP.1997.599617"},{"key":"ref_6","first-page":"309269","article-title":"Improved ESPRIT method for joint direction-of-arrival and frequency estimation using multiple-delay output","volume":"2012","author":"Dong","year":"2012","journal-title":"Int. Antennas J. Propag."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Stein, S., Yair, O., Cohen, D., and Eldar, Y.C. (July, January 28). Joint spectrum sensing and direction of arrival recovery from sub-Nyquist samples. Proceedings of the 2015 IEEE 16th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Stockholm, Sweden.","DOI":"10.1109\/SPAWC.2015.7227054"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2645","DOI":"10.1109\/TSP.2017.2664054","article-title":"CaSCADE: Compressed carrier and DOA estimation","volume":"65","author":"Stein","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1264","DOI":"10.1109\/TSP.2003.810306","article-title":"Analysis of joint angle-frequency estimation using ESPRIT","volume":"51","author":"Lemma","year":"2003","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"7470","DOI":"10.1109\/JSEN.2017.2756861","article-title":"Carrier frequency and DOA estimation of sub-Nyquist sampling multi-band sensor signals","volume":"17","author":"Cui","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2168","DOI":"10.1109\/TSP.2009.2034935","article-title":"DOA estimation of quasi-stationary signals with less sensors than sources and unknown spatial noise covariance: A Khatri\u2013Rao subspace approach","volume":"58","author":"Mao","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"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","first-page":"185","DOI":"10.2528\/PIERM17080306","article-title":"DOA estimation of quasi-stationary signals using a partly-calibrated uniform linear array with fewer sensors than sources","volume":"63","author":"Hsu","year":"2018","journal-title":"Prog. Electromagn. Res. M"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4167","DOI":"10.1109\/TSP.2010.2049264","article-title":"Nested arrays: A novel approach to array processing with enhanced degrees of freedom","volume":"58","author":"Pal","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","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_16","doi-asserted-by":"crossref","unstructured":"Pal, P., and Vaidyanathan, P.P. (2011, January 4\u20137). Coprime sampling and the MUSIC algorithm. Proceedings of the 2011 Digital Signal Processing and Signal Processing Education Meeting (DSP\/SPE), Sedona, AZ, USA.","DOI":"10.1109\/DSP-SPE.2011.5739227"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1109\/LSP.2016.2539324","article-title":"Extension of co-prime arrays based on the fourth-order difference co-array concept","volume":"23","author":"Shen","year":"2016","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"55","DOI":"10.2528\/PIERM18012404","article-title":"DOA estimation using triply primed arrays based on fourth-order statistics","volume":"67","author":"Hsu","year":"2018","journal-title":"Prog. Electromagn. Res. M"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5056","DOI":"10.1109\/TAP.2015.2478475","article-title":"Coupling characterization of a linear dipole array to improve direction-of-arrival estimation","volume":"63","author":"Chen","year":"2015","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1109\/8.827389","article-title":"Compensation for the effects of mutual coupling on direct data domain adaptive algorithms","volume":"48","author":"Adve","year":"2000","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1109\/TWC.2002.800546","article-title":"Experimental study of mutual coupling compensation in smart antenna applications","volume":"1","author":"Dandekar","year":"2002","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4925","DOI":"10.1109\/TSP.2015.2448528","article-title":"Analysis and design of multiple-antenna cognitive radios with multiple primary user signals","volume":"63","author":"McKay","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","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_24","doi-asserted-by":"crossref","first-page":"720","DOI":"10.1109\/29.17564","article-title":"MUSIC, maximum likelihood, and Cramer\u2013Rao bound","volume":"37","author":"Stoica","year":"1989","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1783","DOI":"10.1109\/29.60109","article-title":"Performance study of conditional and unconditional direction-of-arrival estimation","volume":"38","author":"Stoica","year":"1990","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_26","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_27","doi-asserted-by":"crossref","unstructured":"Wang, X., Mao, X., Wang, Y., Zhang, N., and Li, B. (2016). A novel 2-D coherent DOA estimation method based on dimension reduction sparse reconstruction for orthogonal arrays. 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