{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T18:49:12Z","timestamp":1770835752853,"version":"3.50.1"},"reference-count":51,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,3,20]],"date-time":"2022-03-20T00:00:00Z","timestamp":1647734400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003593","name":"National Council for Scientific and Technological Development","doi-asserted-by":"publisher","award":["N\/A"],"award-info":[{"award-number":["N\/A"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100017580","name":"National Education and Research Network","doi-asserted-by":"publisher","award":["01245.010604\/2020-14"],"award-info":[{"award-number":["01245.010604\/2020-14"]}],"id":[{"id":"10.13039\/100017580","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfeicoamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["N\/A"],"award-info":[{"award-number":["N\/A"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Intelligent Reflecting Surfaces (IRSs) are emerging as an effective technology capable of improving the spectral and energy efficiency of future wireless networks. The proposed scenario consists of a multi-antenna base station and a single-antenna user that is assisted by an IRS. The large number of reflecting elements at the IRS and its passive operation represent an important challenge in the acquisition of the instantaneous channel state information (I-CSI) of all links as it adds a very high overhead to the system and requires equipping the IRS with radio-frequency chains. To overcome this problem, a new approach is proposed in order to optimize beamforming at the BS and the phase shifts at the IRS without considering any knowledge of I-CSI but while only exploring the statistical channel state information (S-CSI). We aim at maximizing the user-achievable rate subject to a maximum transmit power constraint. To achieve this goal, we propose a new two-phase framework. In the first phase, both the beamforming at the BS and IRS are designed based only on S-CSI and, in the second phase, the previously designed beamforming pair is used as an initial solution, and beamforming at the BS and IRS is designed only by considering the feedback of the SNR at UE. Moreover, for each phase, we propose new methods based on Genetic Algorithms. Results show that the developed algorithms can approach beamforming with I-CSI but with significantly reduced channel estimation overhead.<\/jats:p>","DOI":"10.3390\/s22062390","type":"journal-article","created":{"date-parts":[[2022,3,20]],"date-time":"2022-03-20T21:37:17Z","timestamp":1647812237000},"page":"2390","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Intelligent Reflecting Surfaces Beamforming Optimization with Statistical Channel Knowledge"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8033-5606","authenticated-orcid":false,"given":"Victoria Dala Pegorara","family":"Souto","sequence":"first","affiliation":[{"name":"Center of Social and Technological Sciences, Catholic University of Pelotas, Pelotas 96015-560, RS, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7389-6245","authenticated-orcid":false,"given":"Richard Demo","family":"Souza","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Federal University of Santa Catarina, Florian\u00f3polis 88040-900, SC, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3727-3988","authenticated-orcid":false,"given":"Bartolomeu F.","family":"Uch\u00f4a-Filho","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Federal University of Santa Catarina, Florian\u00f3polis 88040-900, SC, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yonghui","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, University of Sydney, Sydney, NSW 2006, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"\u00d6zdo\u011fan, \u00d6., and Bj\u00f6rnson, E. 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