{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T10:18:39Z","timestamp":1760955519402},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2014,11,27]],"date-time":"2014-11-27T00:00:00Z","timestamp":1417046400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["EURASIP J. Adv. Signal Process."],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, multi-frequency co-prime arrays are employed to perform direction-of-arrival (DOA) estimation with enhanced degrees of freedom (DOFs). Operation at multiple frequencies creates additional virtual elements in the difference co-array of the co-prime array corresponding to the reference frequency. Sparse reconstruction is then used to fully exploit the enhanced DOFs offered by the multi-frequency co-array, thereby increasing the number of resolvable sources. For the case where the sources have proportional spectra, the received signal vectors at the different frequencies are combined to form an equivalent single measurement vector model corresponding to the multi-frequency co-array. When the sources have nonproportional spectra, a group sparsity-based reconstruction approach is used to determine the direction of signal arrivals. Performance evaluation of the proposed multi-frequency approach is performed using numerical simulations for both cases of proportional and nonproportional source spectra.<\/jats:p>","DOI":"10.1186\/1687-6180-2014-168","type":"journal-article","created":{"date-parts":[[2014,11,27]],"date-time":"2014-11-27T12:01:58Z","timestamp":1417089718000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Sparse reconstruction for direction-of-arrival estimation using multi-frequency co-prime arrays"],"prefix":"10.1186","volume":"2014","author":[{"given":"Elie","family":"BouDaher","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fauzia","family":"Ahmad","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Moeness G","family":"Amin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,11,27]]},"reference":[{"key":"758_CR1","doi-asserted-by":"publisher","DOI":"10.1002\/0471221104","volume-title":"Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory","author":"HL Van Trees","year":"2002","unstructured":"Van Trees HL: Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory. John Wiley and Sons, New York; 2002."},{"key":"758_CR2","volume-title":"Advances in Direction-of-Arrival Estimation","author":"S Chandran","year":"2006","unstructured":"Chandran S: Advances in Direction-of-Arrival Estimation. Artech House, Norwood, MA; 2006."},{"key":"758_CR3","volume-title":"Classical and Modern Direction-of-Arrival Estimation","author":"TE Tuncer","year":"2009","unstructured":"Tuncer TE, Friedlander B: Classical and Modern Direction-of-Arrival Estimation. Academic Press (Elsevier), Boston, MA; 2009."},{"issue":"3","key":"758_CR4","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1109\/TAP.1986.1143830","volume":"34","author":"R Schmidt","year":"1986","unstructured":"Schmidt R: Multiple emitter location and signal parameter estimation. IEEE. Trans. Antenn. Propag. 1986, 34(3):276-280. 10.1109\/TAP.1986.1143830","journal-title":"IEEE. Trans. Antenn. Propag"},{"issue":"7","key":"758_CR5","doi-asserted-by":"publisher","first-page":"984","DOI":"10.1109\/29.32276","volume":"37","author":"R Roy","year":"1989","unstructured":"Roy R, Kailath T: ESPRIT-Estimation of signal parameters via rotational invariance techniques. IEEE. Trans. Acoust. Speech. Signal. Process. 1989, 37(7):984-995. 10.1109\/29.32276","journal-title":"IEEE. Trans. Acoust. Speech. Signal. Process"},{"issue":"2","key":"758_CR6","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1109\/TAP.1968.1139138","volume":"16","author":"A Moffet","year":"1968","unstructured":"Moffet A: Minimum-redundancy linear arrays. IEEE. Trans. Antenn. Propag. 1968, 16(2):172-175. 10.1109\/TAP.1968.1139138","journal-title":"IEEE. Trans. Antenn. Propag"},{"issue":"4","key":"758_CR7","doi-asserted-by":"publisher","first-page":"562","DOI":"10.1109\/PROC.1977.10517","volume":"65","author":"GS Bloom","year":"1977","unstructured":"Bloom GS, Golomb SW: Application of numbered undirected graphs. Proc. IEEE 1977, 65(4):562-570.","journal-title":"Proc. IEEE"},{"issue":"12","key":"758_CR8","doi-asserted-by":"publisher","first-page":"3085","DOI":"10.1109\/78.553482","volume":"44","author":"C Chambers","year":"1996","unstructured":"Chambers C, Tozer TC, Sharman KC, Durrani TS: Temporal and spatial sampling influence on the estimates of superimposed narrowband signals: when less can mean more. IEEE Trans. Signal Process. 1996, 44(12):3085-3098. 10.1109\/78.553482","journal-title":"IEEE Trans. Signal Process"},{"key":"758_CR9","doi-asserted-by":"publisher","first-page":"2165","DOI":"10.1109\/ICASSP.2009.4960046","volume-title":"Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2009","author":"WK Ma","year":"2009","unstructured":"Ma WK, Hsieh TH, Chi CY DOA estimation of quasi-stationary signals via Khatri-Rao subspace. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2009. Taipei, Taiwan; 2009:2165-2168."},{"key":"758_CR10","volume-title":"Array Signal Processing: Concepts and Techniques","author":"DH Johnson","year":"1993","unstructured":"Johnson DH, Dudgeon DE: Array Signal Processing: Concepts and Techniques. Prentice Hall, Englewood, NJ; 1993."},{"issue":"4","key":"758_CR11","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1109\/5.54811","volume":"78","author":"RT Hoctor","year":"1990","unstructured":"Hoctor RT, Kassam SA: The unifying role of the coarray in aperture synthesis for coherent and incoherent imaging. Proc. IEEE 1990, 78(4):735-752. 10.1109\/5.54811","journal-title":"Proc. IEEE"},{"issue":"8","key":"758_CR12","doi-asserted-by":"publisher","first-page":"4167","DOI":"10.1109\/TSP.2010.2049264","volume":"58","author":"P Pal","year":"2010","unstructured":"Pal P, Vaidyanathan PP: Nested arrays: a novel approach to array processing with enhanced degrees of freedom. IEEE Trans. Signal Process. 2010, 58(8):4167-4181.","journal-title":"IEEE Trans. Signal Process"},{"issue":"2","key":"758_CR13","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1109\/TSP.2010.2089682","volume":"59","author":"PP Vaidyanathan","year":"2011","unstructured":"Vaidyanathan PP, Pal P: Sparse sensing with co-prime samplers and arrays. IEEE Trans. Signal Process. 2011, 59(2):573-586.","journal-title":"IEEE Trans. Signal Process"},{"issue":"10","key":"758_CR14","doi-asserted-by":"publisher","first-page":"1522","DOI":"10.1109\/PROC.1985.13324","volume":"73","author":"SU Pillai","year":"1985","unstructured":"Pillai SU, Bar-Ness Y, Haber F: A new approach to array geometry for improved spatial spectrum estimation. Proc. IEEE 1985, 73(10):1522-1524.","journal-title":"Proc. IEEE"},{"key":"758_CR15","first-page":"289","volume-title":"Proceedings of the Digital Signal Processing Workshop and IEEE Signal Processing Education Workshop (DSP\/SPE)","author":"P Pal","year":"2011","unstructured":"Pal P, Vaidyanathan PP Coprime sampling and the MUSIC algorithm. In Proceedings of the Digital Signal Processing Workshop and IEEE Signal Processing Education Workshop (DSP\/SPE). Sedona, AZ; 2011:289-294."},{"issue":"9","key":"758_CR16","doi-asserted-by":"publisher","first-page":"2458","DOI":"10.1109\/78.709534","volume":"46","author":"YI Abramovich","year":"1998","unstructured":"Abramovich YI, Gray DA, Gorokhov AY, Spencer NK: Positive-definite Toeplitz completion in DOA estimation for nonuniform linear antenna arrays. I. Fully augmentable arrays. IEEE Trans. Signal Process. 1998, 46(9):2458-2471. 10.1109\/78.709534","journal-title":"IEEE Trans. Signal Process"},{"issue":"6","key":"758_CR17","doi-asserted-by":"publisher","first-page":"1502","DOI":"10.1109\/78.765119","volume":"47","author":"YI Abramovich","year":"1999","unstructured":"Abramovich YI, Spencer NK, Gorokhov AY: Positive-definite Toeplitz completion in DOA estimation for nonuniform linear antenna arrays. II. Partially augmentable arrays. IEEE Trans. Signal Process. 1999, 47(6):1502-1521. 10.1109\/78.765119","journal-title":"IEEE Trans. Signal Process"},{"key":"758_CR18","volume-title":"Proceedings of the 22nd European Signal Processing Conference (EUSIPCO), 2014","author":"E BouDaher","year":"2014","unstructured":"BouDaher E, Jia Y, Ahmad F, Amin M Direction-of-arrival estimation using multi-frequency co-prime arrays. In Proceedings of the 22nd European Signal Processing Conference (EUSIPCO), 2014. Lisbon, Portugal; 2014."},{"issue":"4","key":"758_CR19","doi-asserted-by":"publisher","first-page":"825","DOI":"10.1117\/1.482668","volume":"7","author":"F Ahmad","year":"1998","unstructured":"Ahmad F, Kassam SA: Performance analysis and array design for wide-band beamformers. J. Electron. Imag. 1998, 7(4):825-838. 10.1117\/1.482668","journal-title":"J. Electron. Imag"},{"key":"758_CR20","first-page":"772","volume-title":"Proceedings of the 43rd Annual Conference on Information Sciences and Systems","author":"JL Moulton","year":"2009","unstructured":"Moulton JL, Kassam SA Resolving more sources with multi-frequency coarrays in high-resolution direction-of-arrival estimation. In Proceedings of the 43rd Annual Conference on Information Sciences and Systems. Baltimore, MD; 2009:772-777."},{"key":"758_CR21","doi-asserted-by":"publisher","first-page":"3967","DOI":"10.1109\/ICASSP.2013.6638403","volume-title":"Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2013","author":"YD Zhang","year":"2013","unstructured":"Zhang YD, Amin MG, Himed B Sparsity-based DOA estimation using co-prime arrays. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2013. Vancouver, Canada; 2013:3967-3971."},{"key":"758_CR22","doi-asserted-by":"publisher","first-page":"958","DOI":"10.1109\/ACSSC.2012.6489158","volume-title":"Proceedings of the 2012 Conference Record of the Forty Six Asilomar Conference on Signals, Systems and Computers (ASILOMAR)","author":"P Pal","year":"2012","unstructured":"Pal P, Vaidyanathan PP On application of LASSO for sparse support recovery with imperfect correlation awareness. In Proceedings of the 2012 Conference Record of the Forty Six Asilomar Conference on Signals, Systems and Computers (ASILOMAR). Pacific Grove, CA; 2012:958-962."},{"issue":"4","key":"758_CR23","doi-asserted-by":"publisher","first-page":"806","DOI":"10.1109\/TASSP.1985.1164649","volume":"33","author":"TJ Shan","year":"1985","unstructured":"Shan TJ, Wax M, Kailath T: On spatial smoothing for direction-of-arrival estimation of coherent signals. IEEE. Trans. Acous. Speech. Signal. Process. 1985, 33(4):806-811. 10.1109\/TASSP.1985.1164649","journal-title":"IEEE. Trans. Acous. Speech. Signal. Process"},{"issue":"2","key":"758_CR24","doi-asserted-by":"publisher","first-page":"760","DOI":"10.1109\/TAES.2013.6494379","volume":"49","author":"N Hu","year":"2013","unstructured":"Hu N, He Z, Xu X, Bao M: DOA estimation for sparse array via sparse signal reconstruction. IEEE. Trans. Aerospace. Electron. Syst. 2013, 49(2):760-773.","journal-title":"IEEE. Trans. Aerospace. Electron. Syst"},{"issue":"4","key":"758_CR25","doi-asserted-by":"publisher","first-page":"823","DOI":"10.1109\/TASSP.1985.1164667","volume":"33","author":"H Wang","year":"1985","unstructured":"Wang H, Kaveh M: Coherent signal-subspace processing for the detection and estimation of angles of arrival of multiple wide-band sources. IEEE. Trans. Acoust. Speech. Signal. Process. 1985, 33(4):823-831. 10.1109\/TASSP.1985.1164667","journal-title":"IEEE. Trans. Acoust. Speech. Signal. Process"},{"issue":"6","key":"758_CR26","doi-asserted-by":"publisher","first-page":"1977","DOI":"10.1109\/TSP.2006.872581","volume":"54","author":"Y Yoon","year":"2006","unstructured":"Yoon Y, Kaplan LM, McClellan JH: TOPS: New DOA estimator for wideband signals. IEEE Trans. Signal Process. 2006, 54(6):1977-1989.","journal-title":"IEEE Trans. Signal Process"},{"issue":"1","key":"758_CR27","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1109\/LSP.2013.2289740","volume":"21","author":"Z Tan","year":"2014","unstructured":"Tan Z, Nehorai A: Sparse direction of arrival estimation using co-prime arrays with off-grid targets. IEEE. Signal. Process. Lett. 2014, 21(1):26-29.","journal-title":"IEEE. Signal. Process. Lett"},{"issue":"8","key":"758_CR28","doi-asserted-by":"publisher","first-page":"3010","DOI":"10.1109\/TSP.2005.850882","volume":"53","author":"D Malioutov","year":"2005","unstructured":"Malioutov D, Cetin M, Willsky A: Sparse signal reconstruction perspective for source localization with sensor arrays. IEEE Trans. Signal Process. 2005, 53(8):3010-3022.","journal-title":"IEEE Trans. Signal Process"},{"issue":"1","key":"758_CR29","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"R Tibshirani","year":"1996","unstructured":"Tibshirani R: Regression shrinkage and selection via the Lasso. J. Roy. Stat. Soc Ser. B. 1996, 58(1):267-288.","journal-title":"J. Roy. Stat. Soc Ser. B"},{"issue":"12","key":"758_CR30","doi-asserted-by":"publisher","first-page":"4655","DOI":"10.1109\/TIT.2007.909108","volume":"53","author":"JA Tropp","year":"2007","unstructured":"Tropp JA, Gilbert AC: Signal recovery from random measurements via orthogonal matching pursuit. IEEE. Trans. Informat. Theory. 2007, 53(12):4655-4666.","journal-title":"IEEE. Trans. Informat. Theory"},{"issue":"3","key":"758_CR31","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1016\/j.acha.2008.07.002","volume":"26","author":"D Needella","year":"2009","unstructured":"Needella D, Tropp JA: CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmonic. Analysis. 2009, 26(3):301-321. 10.1016\/j.acha.2008.07.002","journal-title":"Appl. Comput. Harmonic. Analysis"},{"key":"758_CR32","first-page":"414","volume":"7","author":"VA Morozov","year":"1966","unstructured":"Morozov VA: On the solution of functional equations by the method of regularization. Soviet. Math. Doklady. 1966, 7: 414-417.","journal-title":"Soviet. Math. Doklady"},{"key":"758_CR33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/CBO9780511794308.002","volume-title":"Compressed Sensing: Theory and Applications","author":"M Davenport","year":"2012","unstructured":"Davenport M, Duarte M, Eldar Y, Kutyniok G: Compressed Sensing: Theory and Applications. Cambridge University Press, Cambridge, UK; 2012:1."},{"issue":"1","key":"758_CR34","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1111\/j.1467-9868.2005.00532.x","volume":"68","author":"M Yuan","year":"2007","unstructured":"Yuan M, Lin Y: Model selection and estimation in regression with grouped variables. J. Roy. Stat. Soc. Ser. B. 2007, 68(1):49-67.","journal-title":"J. Roy. Stat. Soc. Ser. B"},{"issue":"6","key":"758_CR35","doi-asserted-by":"publisher","first-page":"3042","DOI":"10.1109\/TSP.2010.2044837","volume":"58","author":"Y Eldar","year":"2010","unstructured":"Eldar Y, Kuppinger P, Bolcskei H: Block-sparsity signals: uncertainty relations and efficient recovery. IEEE Trans. Signal Process. 2010, 58(6):3042-3054.","journal-title":"IEEE Trans. Signal Process"}],"container-title":["EURASIP Journal on Advances in Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/1687-6180-2014-168.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1186\/1687-6180-2014-168\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1687-6180-2014-168.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,5]],"date-time":"2024-06-05T10:51:52Z","timestamp":1717584712000},"score":1,"resource":{"primary":{"URL":"https:\/\/asp-eurasipjournals.springeropen.com\/articles\/10.1186\/1687-6180-2014-168"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11,27]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,12]]}},"alternative-id":["758"],"URL":"https:\/\/doi.org\/10.1186\/1687-6180-2014-168","relation":{},"ISSN":["1687-6180"],"issn-type":[{"value":"1687-6180","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,11,27]]},"assertion":[{"value":"8 July 2014","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 October 2014","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 November 2014","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"168"}}