{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,24]],"date-time":"2025-12-24T12:16:11Z","timestamp":1766578571303,"version":"3.41.2"},"reference-count":14,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2018,8,13]],"date-time":"2018-08-13T00:00:00Z","timestamp":1534118400000},"content-version":"vor","delay-in-days":224,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61401409","61771436"],"award-info":[{"award-number":["61401409","61771436"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002701","name":"Ministry of Education","doi-asserted-by":"publisher","award":["2015R1D1A1A01060057"],"award-info":[{"award-number":["2015R1D1A1A01060057"]}],"id":[{"id":"10.13039\/501100002701","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Wireless Communications and Mobile Computing"],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>Two three\u2010dimensional (3D) 16\u2010ary signal constellations having extended lattice structures are presented in this paper. The theoretical symbol error probabilities (SEPs) of the new constellations in additive white Gaussian noise (AWGN) and Rayleigh fading channel are derived. Computer simulation confirms that the closed\u2010form expressions for average SEPs of the constellations in the AWGN channel are very accurate. The theoretical SEP upper bounds in the Rayleigh fading channel are very tight. Since the presented constellations have larger minimum Euclidean distance (MED) than the conventional one, error performance can be improved up to 0.9\u2009dB in an AWGN environment. Hence, the proposed constellations and their theoretical analysis can be used as a reference for the development of a wireless communication system with 3D signal constellations.<\/jats:p>","DOI":"10.1155\/2018\/7178631","type":"journal-article","created":{"date-parts":[[2018,8,13]],"date-time":"2018-08-13T23:34:01Z","timestamp":1534203241000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["New 3D 16\u2010Ary Signal Constellations and Their Symbol Error Probabilities in AWGN and Rayleigh Fading Channels"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3695-2276","authenticated-orcid":false,"given":"Zhenxing","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiaheng","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuang","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5329-3551","authenticated-orcid":false,"given":"Seog Geun","family":"Kang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,8,13]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1049\/ip-com:20030652"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/50.202809"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCOMM.2009.04.070075"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/LCOMM.2010.02.091347"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1364\/OE.19.022358"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2011.2165062"},{"key":"e_1_2_9_7_2","doi-asserted-by":"crossref","unstructured":"ChenZ.andKangS. 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