{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T07:29:40Z","timestamp":1769930980578,"version":"3.49.0"},"reference-count":20,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2019,10,12]],"date-time":"2019-10-12T00:00:00Z","timestamp":1570838400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["304946\/2016-8"],"award-info":[{"award-number":["304946\/2016-8"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["313239\/2017-7"],"award-info":[{"award-number":["313239\/2017-7"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>We derive exact closed-form expressions for Long Range (LoRa) bit error probability and diversity order for channels subject to Nakagami-m, Rayleigh and Rician fading. Analytical expressions are compared with numerical results, showing the accuracy of our proposed exact expressions. In the limiting case of the Nakagami and Rice parameters, our bit error probability expressions specialize into the non-fading case.<\/jats:p>","DOI":"10.3390\/s19204412","type":"journal-article","created":{"date-parts":[[2019,10,14]],"date-time":"2019-10-14T03:54:13Z","timestamp":1571025253000},"page":"4412","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Bit Error Rate Closed-Form Expressions for LoRa Systems under Nakagami and Rice Fading Channels"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0490-3330","authenticated-orcid":false,"given":"Claudio","family":"Ferreira Dias","sequence":"first","affiliation":[{"name":"Department of Digital Hardware Design, Instituto Eldorado, Eldorado, Alan Turing - 275, Campinas 13083-898, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eduardo","family":"Rodrigues de Lima","sequence":"additional","affiliation":[{"name":"Department of Digital Hardware Design, Instituto Eldorado, Eldorado, Alan Turing - 275, Campinas 13083-898, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gustavo","family":"Fraidenraich","sequence":"additional","affiliation":[{"name":"Department of Communications, University of Campinas, Albert Einstein - 400, Campinas 13083-852, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1109\/MWC.2016.7721743","article-title":"Long-range communications in unlicensed bands: The rising stars in the IoT and smart city scenarios","volume":"23","author":"Centenaro","year":"2016","journal-title":"IEEE Wirel. 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Foundations of Mobile Radio Engineering, Routledge.","DOI":"10.1201\/9780203755563"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/20\/4412\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:25:31Z","timestamp":1760189131000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/20\/4412"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,12]]},"references-count":20,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2019,10]]}},"alternative-id":["s19204412"],"URL":"https:\/\/doi.org\/10.3390\/s19204412","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,12]]}}}