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Optim."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>In this paper, we consider a fundamental problem in modern digital communications known as multiple-input multiple-output (MIMO) detection, which can be formulated as a complex quadratic programming problem subject to unit-modulus and discrete argument constraints. Various semidefinite-relaxation-based (SDR-based) algorithms have been proposed to solve the problem in the literature. In this paper, we first show that conventional SDR is generally not tight for the problem. Then, we propose a new and enhanced SDR and show its tightness under an easily checkable condition, which essentially requires the level of the noise to be below a certain threshold. The above results have answered an open question posed by So in [ Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'10), SIAM, Philadelphia, PA, 2011, pp. 698--711]. Numerical simulation results show that our proposed SDR significantly outperforms the conventional SDR in terms of the relaxation gap.<\/jats:p>","DOI":"10.1137\/17m115075x","type":"journal-article","created":{"date-parts":[[2019,3,5]],"date-time":"2019-03-05T15:51:46Z","timestamp":1551801106000},"page":"719-742","source":"Crossref","is-referenced-by-count":25,"title":["Tightness of a New and Enhanced Semidefinite Relaxation for MIMO Detection"],"prefix":"10.1137","volume":"29","author":[{"given":"Cheng","family":"Lu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9684-9150","authenticated-orcid":true,"given":"Ya-Feng","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei-Qiang","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5838-1676","authenticated-orcid":true,"given":"Shuzhong","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,3,5]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02614432"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-016-1059-6"},{"key":"atypb3","first-page":"1265","volume":"35","author":"Bandeira A. 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