{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,26]],"date-time":"2026-04-26T06:02:48Z","timestamp":1777183368120,"version":"3.51.4"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T00:00:00Z","timestamp":1675814400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T00:00:00Z","timestamp":1675814400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key R &D Program of China","doi-asserted-by":"crossref","award":["2018YFE0126300"],"award-info":[{"award-number":["2018YFE0126300"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U21A20456"],"award-info":[{"award-number":["U21A20456"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61901413"],"award-info":[{"award-number":["61901413"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Zhejiang University Education Foundation Qizhen Scholar Foundation"},{"name":"5G Open Laboratory of Hangzhou Future Sci-Tech City"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["EURASIP J. Adv. Signal Process."],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Conventional direction-of-arrival (DOA) estimation methods for multiple-input multiple-output (MIMO) joint sensing and communication system normally pursue high estimation accuracy and resolution by imposing orthogonal waveforms. However, such operation results in a deterioration of communication performance. In this paper, we propose a nonorthogonal waveform assisted DOA estimation algorithm, where an augmented virtual array is derived by exploiting the nonorthogonal MIMO communication waveforms, while a high communication rate can still be maintained. To estimate the round-trip sensing channels of each subcarrier, we utilize the transmitted symbols as pilot symbols, and obtain all the channel coefficients with a minimum mean square error solver. A virtual channel matrix can be formulated with these channel coefficients, which can be regarded as the samples of an augmented virtual array. Based on that, the subspace processing can be conducted for DOA estimation with fully nonorthogonal waveforms. Furthermore, the rank deficiency property of the equivalent signal matrix of the virtual array is analyzed when the distance of targets are identical. To address the problem, a Toeplitz reconstruction method is proposed to restore the rank of the rank-deficient equivalent signal matrix for DOA estimation. Simulations show that the proposed nonorthogonal waveform assisted DOA estimation algorithm outperforms the conventional methods in terms of resolution and accuracy, while maintaining a satisfactory computational efficiency.<\/jats:p>","DOI":"10.1186\/s13634-023-00976-6","type":"journal-article","created":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T09:04:22Z","timestamp":1675847062000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Nonorthogonal waveform assisted DOA estimation for joint MIMO sensing and communication"],"prefix":"10.1186","volume":"2023","author":[{"given":"Luning","family":"Lin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hang","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9437-2379","authenticated-orcid":false,"given":"Chengwei","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shibo","family":"He","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiguo","family":"Shi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,2,8]]},"reference":[{"issue":"1","key":"976_CR1","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1109\/COMST.2021.3122519","volume":"24","author":"JA Zhang","year":"2022","unstructured":"J.A. Zhang, M.L. Rahman, K. Wu, X. Huang, Y.J. Guo, S. Chen, J. Yuan, Enabling joint communication and radar sensing in mobile networks\u2013A survey. IEEE Commun. Surv. Tut. 24(1), 306\u2013345 (2022)","journal-title":"IEEE Commun. Surv. Tut."},{"issue":"5","key":"976_CR2","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1109\/MSP.2019.2907329","volume":"36","author":"L Zheng","year":"2019","unstructured":"L. Zheng, M. Lops, Y.C. Eldar, X. Wang, Radar and communication coexistence: An overview: A review of recent methods. IEEE Signal Process. Mag. 36(5), 85\u201399 (2019)","journal-title":"IEEE Signal Process. Mag."},{"issue":"8","key":"976_CR3","doi-asserted-by":"publisher","first-page":"2168","DOI":"10.1109\/TSP.2015.2505667","volume":"64","author":"A Hassanien","year":"2016","unstructured":"A. Hassanien, M.G. Amin, Y.D. Zhang, F. Ahmad, Dual-function radar-communications: Information embedding using sidelobe control and waveform diversity. IEEE Trans. Signal Process. 64(8), 2168\u20132181 (2016)","journal-title":"IEEE Trans. Signal Process."},{"issue":"5","key":"976_CR4","doi-asserted-by":"publisher","first-page":"1316","DOI":"10.1109\/TSP.2017.2770086","volume":"66","author":"C Shi","year":"2018","unstructured":"C. Shi, F. Wang, M. Sellathurai, J. Zhou, S. Salous, Power minimization-based robust OFDM radar waveform design for radar and communication systems in coexistence. IEEE Trans. Signal Process. 66(5), 1316\u20131330 (2018)","journal-title":"IEEE Trans. Signal Process."},{"issue":"6","key":"976_CR5","doi-asserted-by":"publisher","first-page":"1728","DOI":"10.1109\/JSAC.2022.3156632","volume":"40","author":"F Liu","year":"2022","unstructured":"F. Liu, Y. Cui, C. Masouros, J. Xu, T.X. Han, Y.C. Eldar, S. Buzzi, Integrated sensing and communications: Toward dual-functional wireless networks for 6G and beyond. IEEE J. Sel. Areas Commun. 40(6), 1728\u20131767 (2022)","journal-title":"IEEE J. Sel. Areas Commun."},{"issue":"10","key":"976_CR6","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1109\/MAES.2016.150225","volume":"31","author":"A Hassanien","year":"2016","unstructured":"A. Hassanien, M.G. Amin, Y.D. Zhang, F. Ahmad, Signaling strategies for dual-function radar communications: An overview. IEEE Aerosp. Electron. Syst. Mag. 31(10), 36\u201345 (2016)","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"issue":"3","key":"976_CR7","doi-asserted-by":"publisher","first-page":"1926","DOI":"10.1109\/TAES.2019.2939611","volume":"56","author":"ML Rahman","year":"2020","unstructured":"M.L. Rahman, J.A. Zhang, X. Huang, Y.J. Guo, R.W. Heath, Framework for a perceptive mobile network using joint communication and radar sensing. IEEE Trans. Aerosp. Electron. Syst. 56(3), 1926\u20131941 (2020)","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"issue":"8","key":"976_CR8","doi-asserted-by":"publisher","first-page":"6256","DOI":"10.1109\/TWC.2022.3148035","volume":"21","author":"A Sakhnini","year":"2022","unstructured":"A. Sakhnini, S. De Bast, M. Guenach, A. Bourdoux, H. Sahli, S. Pollin, Near-field coherent radar sensing using a massive MIMO communication testbed. IEEE Trans. Wireless Commun. 21(8), 6256\u20136270 (2022)","journal-title":"IEEE Trans. Wireless Commun."},{"key":"976_CR9","doi-asserted-by":"publisher","first-page":"2576","DOI":"10.1109\/TSP.2022.3173150","volume":"70","author":"Z Mao","year":"2022","unstructured":"Z. Mao, S. Liu, Y.D. Zhang, L. Han, Y. Huang, Joint DoA-range estimation using space-frequency virtual difference coarray. IEEE Trans. Signal Process. 70, 2576\u20132592 (2022)","journal-title":"IEEE Trans. Signal Process."},{"issue":"2","key":"976_CR10","doi-asserted-by":"publisher","first-page":"870","DOI":"10.1109\/COMST.2017.2783541","volume":"20","author":"IA Hemadeh","year":"2018","unstructured":"I.A. Hemadeh, K. Satyanarayana, M. El-Hajjar, L. Hanzo, Millimeter-wave communications: Physical channel models, design considerations, antenna constructions, and link-budget. IEEE Commun. Surv. Tut. 20(2), 870\u2013913 (2018)","journal-title":"IEEE Commun. Surv. Tut."},{"issue":"4","key":"976_CR11","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1109\/74.951559","volume":"43","author":"M Steinbauer","year":"2001","unstructured":"M. Steinbauer, A.F. Molisch, E. Bonek, The double-directional radio channel. IEEE Antennas Propag. Mag. 43(4), 51\u201363 (2001)","journal-title":"IEEE Antennas Propag. Mag."},{"key":"976_CR12","doi-asserted-by":"publisher","first-page":"5935","DOI":"10.1109\/TSP.2021.3122292","volume":"69","author":"S Zhang","year":"2021","unstructured":"S. Zhang, A. Ahmed, Y.D. Zhang, S. Sun, Enhanced DOA estimation exploiting multi-frequency sparse array. IEEE Trans. Signal Process. 69, 5935\u20135946 (2021)","journal-title":"IEEE Trans. Signal Process."},{"issue":"22","key":"976_CR13","doi-asserted-by":"publisher","first-page":"5956","DOI":"10.1109\/TSP.2018.2872012","volume":"66","author":"C Zhou","year":"2018","unstructured":"C. Zhou, Y. Gu, X. Fan, Z. Shi, G. Mao, Y.D. Zhang, Direction-of-arrival estimation for coprime array via virtual array interpolation. IEEE Trans. Signal Process. 66(22), 5956\u20135971 (2018)","journal-title":"IEEE Trans. Signal Process."},{"key":"976_CR14","doi-asserted-by":"crossref","unstructured":"Z. Ni, J.A. Zhang, X. Huang, K. Yang, F. Gao, Parameter estimation and signal optimization for joint communication and radar sensing. In Proc. IEEE Int. Conf. Commun. Workshops (ICC), (Dublin, Ireland, 2020), pp. 1\u20136","DOI":"10.1109\/ICCWorkshops49005.2020.9145109"},{"issue":"11","key":"976_CR15","doi-asserted-by":"publisher","first-page":"1710","DOI":"10.1109\/LSP.2018.2872400","volume":"25","author":"C Zhou","year":"2018","unstructured":"C. Zhou, Y. Gu, Z. Shi, Y.D. Zhang, Off-grid direction-of-arrival estimation using coprime array interpolation. IEEE Signal Process. Lett. 25(11), 1710\u20131714 (2018)","journal-title":"IEEE Signal Process. Lett."},{"issue":"6","key":"976_CR16","doi-asserted-by":"publisher","first-page":"1393","DOI":"10.1109\/JSTSP.2021.3109431","volume":"15","author":"MF Keskin","year":"2021","unstructured":"M.F. Keskin, H. Wymeersch, V. Koivunen, MIMO-OFDM joint radar-communications: Is ICI friend or foe? IEEE J. Sel. Topics Signal Process. 15(6), 1393\u20131408 (2021)","journal-title":"IEEE J. Sel. Topics Signal Process."},{"issue":"7","key":"976_CR17","doi-asserted-by":"publisher","first-page":"3881","DOI":"10.1109\/TSP.2012.2194289","volume":"60","author":"Y Gu","year":"2012","unstructured":"Y. Gu, A. Leshem, Robust adaptive beamforming based on interference covariance matrix reconstruction and steering vector estimation. IEEE Trans. Signal Process. 60(7), 3881\u20133885 (2012)","journal-title":"IEEE Trans. Signal Process."},{"key":"976_CR18","doi-asserted-by":"publisher","first-page":"1634","DOI":"10.1109\/LSP.2022.3190768","volume":"29","author":"H Zheng","year":"2022","unstructured":"H. Zheng, C. Zhou, Z. Shi, Y. Gu, Structured tensor reconstruction for coherent DOA estimation. IEEE Signal Process. Lett. 29, 1634\u20131638 (2022)","journal-title":"IEEE Signal Process. Lett."},{"issue":"2","key":"976_CR19","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1109\/JPROC.2003.821912","volume":"92","author":"GL Stuber","year":"2004","unstructured":"G.L. Stuber, J.R. Barry, S.W. McLaughlin, Y. Li, M.A. Ingram, T.G. Pratt, Broadband MIMO-OFDM wireless communications. Proc. IEEE 92(2), 271\u2013294 (2004)","journal-title":"Proc. IEEE"},{"key":"976_CR20","doi-asserted-by":"crossref","unstructured":"S.D. Liyanaarachchi, C. Baquero Barneto, T. Riihonen, M. Heino, M. Valkama, Range\u2013angle processing for target detection in joint MIMO-OFDM communications and sensing. In Proc. IEEE  Workshop Signal Process. Adv. Wireless Commun. (SPAWC), (Lucca, Italy, 2021), pp. 486\u2013490","DOI":"10.1109\/SPAWC51858.2021.9593229"},{"key":"976_CR21","doi-asserted-by":"crossref","unstructured":"L. Pucci, E. Matricardi, E. Paolini, W. Xu, A. Giorgetti, Performance analysis of joint sensing and communication based on 5G New Radio. In Proc. IEEE Glob. Commun. Conf. (GLOBECOM), (Madrid, Spain, 2021), pp. 1\u20136","DOI":"10.1109\/GCWkshps52748.2021.9682124"},{"issue":"7","key":"976_CR22","doi-asserted-by":"publisher","first-page":"2043","DOI":"10.1109\/JSAC.2022.3155522","volume":"40","author":"L Pucci","year":"2022","unstructured":"L. Pucci, E. Paolini, A. Giorgetti, System-level analysis of joint sensing and communication based on 5G New Radio. IEEE J. Sel. Areas Commun. 40(7), 2043\u20132055 (2022)","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"976_CR23","doi-asserted-by":"publisher","first-page":"1287","DOI":"10.1109\/TSP.2021.3057499","volume":"69","author":"Z Ni","year":"2021","unstructured":"Z. Ni, J.A. Zhang, X. Huang, K. Yang, J. Yuan, Uplink sensing in perceptive mobile networks with asynchronous transceivers. IEEE Trans. Signal Process. 69, 1287\u20131300 (2021)","journal-title":"IEEE Trans. Signal Process."},{"key":"976_CR24","doi-asserted-by":"crossref","unstructured":"L. Pucci, E. Matricardi, E. Paolini, W. Xu, A. Giorgetti, Performance analysis of a bistatic joint sensing and communication system. In Proc. IEEE Int. Conf. Commun. Workshops (ICC), (Seoul, Korea, 2022), pp. 73\u201378","DOI":"10.1109\/ICCWorkshops53468.2022.9814645"},{"issue":"5","key":"976_CR25","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1109\/MSP.2007.904812","volume":"24","author":"J Li","year":"2007","unstructured":"J. Li, P. Stoica, MIMO radar with colocated antennas. IEEE Signal Process. Mag. 24(5), 106\u2013114 (2007)","journal-title":"IEEE Signal Process. Mag."},{"key":"976_CR26","doi-asserted-by":"crossref","unstructured":"C. Sturm, T. Zwick, W. Wiesbeck, An OFDM system concept for joint radar and communications operations. In Proc. IEEE Veh. Technol. Conf. (VTC), (Barcelona, Spain, 2009), pp. 1\u20135","DOI":"10.1109\/VETECS.2009.5073387"},{"issue":"7","key":"976_CR27","doi-asserted-by":"publisher","first-page":"1236","DOI":"10.1109\/JPROC.2011.2131110","volume":"99","author":"C Sturm","year":"2011","unstructured":"C. Sturm, W. Wiesbeck, Waveform design and signal processing aspects for fusion of wireless communications and radar sensing. Proc. IEEE 99(7), 1236\u20131259 (2011)","journal-title":"Proc. IEEE"},{"issue":"2","key":"976_CR28","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1007\/s11045-018-0576-2","volume":"30","author":"Y Liu","year":"2019","unstructured":"Y. Liu, G. Liao, Z. Yang, J. Xu, Joint range and angle estimation for an integrated system combining MIMO radar with OFDM communication. Multidimens. Syst. Signal Process. 30(2), 661\u2013687 (2019)","journal-title":"Multidimens. Syst. Signal Process."},{"key":"976_CR29","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1016\/j.dsp.2018.08.016","volume":"83","author":"X Wang","year":"2018","unstructured":"X. Wang, A. Hassanien, M.G. Amin, Sparse transmit array design for dual-function radar communications by antenna selection. Digit. Signal Process. 83, 223\u2013234 (2018)","journal-title":"Digit. Signal Process."},{"issue":"6","key":"976_CR30","doi-asserted-by":"publisher","first-page":"1890","DOI":"10.1109\/JSAC.2022.3155529","volume":"40","author":"Z Cheng","year":"2022","unstructured":"Z. Cheng, B. Liao, QoS-aware hybrid beamforming and DOA estimation in multi-carrier dual-function radar-communication systems. IEEE J. Sel. Areas Commun. 40(6), 1890\u20131905 (2022)","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"976_CR31","unstructured":"Z. Xu, A. Petropulu, A wideband dual function radar communication system with sparse array and OFDM waveforms. arXiv: 2106.05878 (2021)"},{"issue":"4","key":"976_CR32","doi-asserted-by":"publisher","first-page":"2091","DOI":"10.1109\/TAES.2018.2847958","volume":"54","author":"B Liao","year":"2018","unstructured":"B. Liao, Fast angle estimation for MIMO radar with nonorthogonal waveforms. IEEE Trans. Aerosp. Electron. Syst. 54(4), 2091\u20132096 (2018)","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"issue":"2","key":"976_CR33","doi-asserted-by":"publisher","first-page":"414","DOI":"10.1109\/LCOMM.2016.2622691","volume":"21","author":"G Zheng","year":"2017","unstructured":"G. Zheng, DOA estimation in MIMO radar with non-perfectly orthogonal waveforms. IEEE Commun. Lett. 21(2), 414\u2013417 (2017)","journal-title":"IEEE Commun. Lett."},{"key":"976_CR34","doi-asserted-by":"publisher","first-page":"1545","DOI":"10.1109\/LSP.2021.3099074","volume":"28","author":"H Zheng","year":"2021","unstructured":"H. Zheng, Z. Shi, C. Zhou, M. Haardt, J. Chen, Coupled coarray tensor CPD for DOA estimation with coprime L-shaped array. IEEE Signal Process. Lett. 28, 1545\u20131549 (2021)","journal-title":"IEEE Signal Process. Lett."},{"issue":"3","key":"976_CR35","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1109\/JSEN.2016.2637059","volume":"17","author":"Z Shi","year":"2017","unstructured":"Z. Shi, C. Zhou, Y. Gu, N.A. Goodman, F. Qu, Source estimation using coprime array: A sparse reconstruction perspective. IEEE Sensors J. 17(3), 755\u2013765 (2017)","journal-title":"IEEE Sensors J."},{"issue":"2","key":"976_CR36","doi-asserted-by":"publisher","first-page":"1099","DOI":"10.1109\/TVT.2017.2704610","volume":"67","author":"C Zhou","year":"2018","unstructured":"C. Zhou, Y. Gu, S. He, Z. Shi, A robust and efficient algorithm for coprime array adaptive beamforming. IEEE Trans. Veh. Technol. 67(2), 1099\u20131112 (2018)","journal-title":"IEEE Trans. Veh. Technol."},{"issue":"2","key":"976_CR37","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1049\/iet-spr.2016.0185","volume":"11","author":"V Savaux","year":"2017","unstructured":"V. Savaux, Y. Lou\u00ebt, LMMSE channel estimation in OFDM context: A review. IET Signal Process. 11(2), 123\u2013134 (2017)","journal-title":"IET Signal Process."},{"issue":"4","key":"976_CR38","doi-asserted-by":"publisher","first-page":"1891","DOI":"10.1109\/COMST.2014.2320074","volume":"16","author":"Y Liu","year":"2014","unstructured":"Y. Liu, Z. Tan, H. Hu, L.J. Cimini, G.Y. Li, Channel estimation for OFDM. IEEE Commun. Surv. Tut. 16(4), 1891\u20131908 (2014)","journal-title":"IEEE Commun. Surv. Tut."},{"key":"976_CR39","unstructured":"3GPP: NR; User Equipment (UE) radio transmission and reception; Part 1: Range 1 Standalone. Technical Specification (TS) 38.101-1, 3rd Generation Partnership Project (3GPP) (2021). Version 17.3.0. http:\/\/www.3gpp.org\/-DynaReport\/-38101-1.htm"}],"container-title":["EURASIP Journal on Advances in Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13634-023-00976-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s13634-023-00976-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13634-023-00976-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T09:10:28Z","timestamp":1675847428000},"score":1,"resource":{"primary":{"URL":"https:\/\/asp-eurasipjournals.springeropen.com\/articles\/10.1186\/s13634-023-00976-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,8]]},"references-count":39,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["976"],"URL":"https:\/\/doi.org\/10.1186\/s13634-023-00976-6","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-1939389\/v1","asserted-by":"object"}]},"ISSN":["1687-6180"],"issn-type":[{"value":"1687-6180","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,8]]},"assertion":[{"value":"10 August 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 January 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 February 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The authors declare that they have no competing interests.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"22"}}