{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T20:01:09Z","timestamp":1784232069085,"version":"3.55.0"},"reference-count":39,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T00:00:00Z","timestamp":1740096000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico (CNPq)","award":["312501\/2021-8"],"award-info":[{"award-number":["312501\/2021-8"]}]},{"name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico (CNPq)","award":["001"],"award-info":[{"award-number":["001"]}]},{"name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior (CAPES)","award":["312501\/2021-8"],"award-info":[{"award-number":["312501\/2021-8"]}]},{"name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior (CAPES)","award":["001"],"award-info":[{"award-number":["001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper analyzes for the first time how the Beckmann distribution can be used to characterize the random variable that represents the envelope of the effective channel gain experienced by the k-th user equipment (UE) of a user-centric (UC) cell-free (CF) system in a scenario with noisy channel state information (CSI) estimation and line of sight (LoS). Additionally, it is shown how the Beckmann probability density function (PDF) can be used to derive the PDF and the cumulative density function (CDF) of the instantaneous signal-to-interference-plus-noise ratio (SINR) of the UC CF k-th UE, followed by applications in the ergodic capacity (EC) and outage probability (OP) expression derivations. It is shown that, regardless of the type of distribution considered for the channel gain between each access point (AP) and UE links, the effective gain presents a Beckmann distribution.<\/jats:p>","DOI":"10.3390\/e27030223","type":"journal-article","created":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:39:07Z","timestamp":1740119947000},"page":"223","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["User-Centric Cell-Free Massive Multiple-Input-Multiple-Output System with Noisy Channel Gain Estimation and Line of Sight: A Beckmann Distribution Approach"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1699-8883","authenticated-orcid":false,"given":"Danilo B. T.","family":"Almeida","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Federal University of Campina Grande, Campina Grande 58429-900, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2849-1644","authenticated-orcid":false,"given":"Marcelo S.","family":"Alencar","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Federal University of Para\u00edba, Jo\u00e3o Pessoa 58051-970, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5065-2221","authenticated-orcid":false,"given":"Wamberto J. L.","family":"Queiroz","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Federal University of Campina Grande, Campina Grande 58429-900, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9274-7838","authenticated-orcid":false,"given":"Rafael M.","family":"Duarte","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Federal University of Vale do S\u00e3o Francisco, Petrolina 56304-917, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6123-0390","authenticated-orcid":false,"given":"Francisco","family":"Madeiro","sequence":"additional","affiliation":[{"name":"Polytechnic School of Pernambuco, University of Pernambuco, Recife 50720-001, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ngo, H.Q., Ashikhmin, A., Yang, H., Larsson, E.G., and Marzetta, T.L. 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