{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T02:52:46Z","timestamp":1767840766586,"version":"3.49.0"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2016,2,19]],"date-time":"2016-02-19T00:00:00Z","timestamp":1455840000000},"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>Underwater acoustic sensor networks are a promising technology that allow real-time data collection in seas and oceans for a wide variety of applications. Smaller size and weight sensors can be achieved with working frequencies shifted from audio to the ultrasonic band. At these frequencies, the fading phenomena has a significant presence in the channel behavior, and the design of a reliable communication link between the network sensors will require a precise characterization of it. Fading in underwater channels has been previously measured and modeled in the audio band. However, there have been few attempts to study it at ultrasonic frequencies. In this paper, a campaign of measurements of ultrasonic underwater acoustic channels in Mediterranean shallow waters conducted by the authors is presented. These measurements are used to determine the parameters of the so-called \u03ba-\u03bc shadowed distribution, a fading model with a direct connection to the underlying physical mechanisms. The model is then used to evaluate the capacity of the measured channels with a closed-form expression.<\/jats:p>","DOI":"10.3390\/s16020256","type":"journal-article","created":{"date-parts":[[2016,2,19]],"date-time":"2016-02-19T11:29:39Z","timestamp":1455881379000},"page":"256","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["Measurement and Modeling of Narrowband Channels for Ultrasonic Underwater Communications"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4871-5609","authenticated-orcid":false,"given":"Francisco","family":"Ca\u00f1ete","sequence":"first","affiliation":[{"name":"Departamento de Ingenier\u00eda de Comunicaciones, ETS Ingenier\u00eda de Telecomunicaci\u00f3n, Universidad de M\u00e1laga, M\u00e1laga 29071, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3391-9836","authenticated-orcid":false,"given":"Jes\u00fas","family":"L\u00f3pez-Fern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda de Comunicaciones, ETS Ingenier\u00eda de Telecomunicaci\u00f3n, Universidad de M\u00e1laga, M\u00e1laga 29071, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Celia","family":"Garc\u00eda-Corrales","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda de Comunicaciones, ETS Ingenier\u00eda de Telecomunicaci\u00f3n, Universidad de M\u00e1laga, M\u00e1laga 29071, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonio","family":"S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Sociedad An\u00f3nima de Electr\u00f3nica Submarina (SAES), Cartagena 30205, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Encarnaci\u00f3n","family":"Robles","sequence":"additional","affiliation":[{"name":"Sociedad An\u00f3nima de Electr\u00f3nica Submarina (SAES), Cartagena 30205, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francisco","family":"Rodrigo","sequence":"additional","affiliation":[{"name":"Sociedad An\u00f3nima de Electr\u00f3nica Submarina (SAES), Cartagena 30205, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9","family":"Paris","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda de Comunicaciones, ETS Ingenier\u00eda de Telecomunicaci\u00f3n, Universidad de M\u00e1laga, M\u00e1laga 29071, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,2,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2580","DOI":"10.1121\/1.2782884","article-title":"A high-frequency warm shallow water acoustic communications channel model and measurements","volume":"122","author":"Chitre","year":"2007","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1109\/MCOM.2009.4752682","article-title":"Underwater acoustic communication channels: Propagation models and statistical characterization","volume":"47","author":"Stojanovic","year":"2009","journal-title":"IEEE Commun. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1109\/JOE.2013.2278913","article-title":"Propagation and scattering effects in inderwater acoustc communication channels","volume":"38","year":"2013","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_4","unstructured":"Chitre, M., Potter, J., and Ong, S.H. (2004, January 9\u201312). Underwater acoustic channel characterisation for medium-range shallow water communications. Proceedings of the MTTS\/IEEE Techno-Ocean\u201904, Kobe, Japan."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2615","DOI":"10.1121\/1.2346133","article-title":"High-frequency channel characterization for M-ary frequency-shift-keying underwater acoustic communications","volume":"120","author":"Yang","year":"2006","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Hicheri, R., P\u00e4tzol, M., Talha, B., and Youssef, N. (2014, January 19\u201321). A study on the distribution of the envelope and the capacity of underwater acoustic channels. Proceedings of the 14th IEEE International Conference on Communication Systems, Macau, China.","DOI":"10.1109\/ICCS.2014.7024832"},{"key":"ref_7","unstructured":"Kim, S.M., Byun, S.H., Kim, S.G., Kim, D.J., Kim, S., and Lim, Y.K. (2013, January 23\u201326). Underwater acoustic channel characterization at 6 kHz and 12 kHz in a shallow water near Jeju Island. Proceedings of the MTS\/IEEE Oceans Conference, San Diego, CA, USA."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Kulhandjian, H., and Melodia, T. (2014, January 12\u201314). Modeling underwater acoustic channels in short-range shallow water enviroments. Proceedings of the International Conference on Underwater Networks and Systems, Rome, Italy.","DOI":"10.1145\/2671490.2674560"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1109\/JOE.2013.2278787","article-title":"Statistical characterization and computationally efficient modeling of a class of underwater acoustic communication channels","volume":"38","author":"Qarabaqi","year":"2013","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1049\/iet-com.2014.0456","article-title":"Short-term fading model for signals reflected by ocean surfaces in underwater acoustic communications","volume":"9","author":"Kim","year":"2015","journal-title":"IET Commun."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hajenko, T.J., and Benson, C.R. (2010, January 24\u201327). The high frequency underwater acoustic channel. Proceedings of the IEEE Oceans Conference, Sydney, Australia.","DOI":"10.1109\/OCEANSSYD.2010.5603801"},{"key":"ref_12","unstructured":"Ainslie, M.A., Dahl, P.H., de Jong, C.A.F., and Laws, R.M. (2014, January 22\u201327). Practical spreading laws: The snakes and ladders of shallow water acoustics. Proceedings of the 2nd International Conference and Exhibition on Underwater Acoustics, Rhodes, Greece."},{"key":"ref_13","unstructured":"Rappaport, T.S. (1996). Wireless Communications: Principles and Practice, Prentice Hall."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Goldsmith, A. (2005). Wireless Communications, Cambridge University Press.","DOI":"10.1017\/CBO9780511841224"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Simon, M.K., and Alouini, M.S. (2004). Digital Communication over Fading Channels, John Wiley & Sons Inc.. [2nd ed.].","DOI":"10.1002\/0471715220"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Borowski, B. (2009, January 26\u201329). Characterization of a very shallow water acoustic communication channel. Proceedings of the MTS\/IEEE Oceans Conference, Boloxi, MS, USA.","DOI":"10.23919\/OCEANS.2009.5422360"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1109\/MAP.2007.370983","article-title":"The \u03ba-\u03bc and the \u03b7-\u03bc distribution","volume":"49","author":"Yacoub","year":"2007","journal-title":"IEEE Antennas Propag. Mag."},{"key":"ref_18","unstructured":"Zhang, J., Cross, J., and Zheng, Y.R. (November, January 31). Statistical channel modeling of wireless shallow water acoustic communications for experimental data. Proceedings of the IEEE Military Communication Conference, San Jose, CA, USA."},{"key":"ref_19","unstructured":"Ruiz-Vega, F., Clemente, M.C., Paris, J.F., and Otero, P. (2012, January 12\u201314). Rician shadowed statistical characterization of shallow water acoustic channels for wireless communications. Proceedings of the UComms Conference, Sestri, Italy."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1109\/TVT.2013.2281213","article-title":"Statistical characterization of \u03ba-\u03bc shadowed fading channels","volume":"63","author":"Paris","year":"2014","journal-title":"IEEE Trans.Veh. Technol."},{"key":"ref_21","unstructured":"S\u00e1nchez, A., Robles, E., Rodrigo, F.J., Ruiz-Vega, F., Fern\u00e1ndez-Plazaola, U., and Paris, J.F. (2014, January 22\u201327). Measurement and modeling of fading in ultrasonic underwater channels. Proceedings of the 2nd International Conference and Exhibition on Underwater Acoustic, Rhodes, Greece."},{"key":"ref_22","unstructured":"Gradshteyn, I., and Ryzhik, I.M. (2007). Tables of Integrals, Series and Products, Academic Press. [7th ed.]."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Corder, G.W., and Foreman, D.I. (2009). Nonparametric Statistics for Non-Statisticians: A Step-by-Step Approach, John Wiley & Sons Inc.","DOI":"10.1002\/9781118165881"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Garc\u00eda-Corrales, C., Ca\u00f1ete, F.J., and Paris, J.F. (2014). Capacity of \u03ba-\u03bc Shadowed Fading Channels. Int. J. Antennas Propag., 2014.","DOI":"10.1155\/2014\/975109"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/2\/256\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:19:24Z","timestamp":1760210364000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/2\/256"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,19]]},"references-count":24,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,2]]}},"alternative-id":["s16020256"],"URL":"https:\/\/doi.org\/10.3390\/s16020256","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,2,19]]}}}