{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:24:48Z","timestamp":1760239488972,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2020,11,22]],"date-time":"2020-11-22T00:00:00Z","timestamp":1606003200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Large intelligent surfaces (LIS) promises not only to improve the signal to noise ratio, and spectral efficiency but also to reduce the energy consumption during the transmission. We consider a base station equipped with an antenna array using the maximum ratio transmission (MRT), and a large reflector array sending signals to a single user. Each subchannel is affected by the Rayleigh flat fading, and the reflecting elements perform non-perfect phase correction which introduces a Von Mises distributed phase error. Based on the central limit theorem (CLT), we conclude that the overall channel has an equivalent Gamma fading whose parameters are derived from the moments of the channel fading between the antenna array and LIS, and also from the LIS to the single user. Assuming that the equivalent channel can be modeled as a Gamma distribution, we propose very accurate closed-form expressions for the bit error probability and a very tight upper bound. For the case where the LIS is not able to perform perfect phase cancellation, that is, under phase errors, it is possible to analyze the system performance considering the analytical approximations and the simulated results obtained using the well known Monte Carlo method. The analytical expressions for the parameters of the Gamma distribution are very difficult to be obtained due to the complexity of the nonlinear transformations of random variables with non-zero mean and correlated terms. Even with perfect phase cancellation, all the fading coefficients are complex due to the link between the user and the base station that is not neglected in this paper.<\/jats:p>","DOI":"10.3390\/s20226679","type":"journal-article","created":{"date-parts":[[2020,11,23]],"date-time":"2020-11-23T01:28:48Z","timestamp":1606094928000},"page":"6679","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Large Intelligent Surfaces Communicating Through Massive MIMO Rayleigh Fading Channels"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9309-1735","authenticated-orcid":false,"given":"Ricardo","family":"Coelho Ferreira","sequence":"first","affiliation":[{"name":"DECOM\/FEEC, State University of Campinas, Av. Albert Einstein 400, Campinas 13083-970, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0785-9606","authenticated-orcid":false,"given":"Michelle S. P.","family":"Facina","sequence":"additional","affiliation":[{"name":"DECOM\/FEEC, State University of Campinas, Av. Albert Einstein 400, Campinas 13083-970, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2167-7286","authenticated-orcid":false,"given":"Felipe A. P.","family":"de Figueiredo","sequence":"additional","affiliation":[{"name":"Instituto Nacional de Telecomunica\u00e7\u00f5es, Santa Rita do Sapuca\u00ed 37540-000, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0517-1496","authenticated-orcid":false,"given":"Gustavo","family":"Fraidenraich","sequence":"additional","affiliation":[{"name":"DECOM\/FEEC, State University of Campinas, Av. Albert Einstein 400, Campinas 13083-970, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4268-9726","authenticated-orcid":false,"given":"Eduardo Rodrigues","family":"de Lima","sequence":"additional","affiliation":[{"name":"Department of Hardware Design, Instituto de Pesquisas Eldorado, Campinas 3083-898, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/MVT.2019.2921208","article-title":"6G wireless networks: Vision, requirements, architecture, and key technologies","volume":"14","author":"Zhang","year":"2019","journal-title":"IEEE Veh. Technol. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Fernando, X., and Farahneh, H. (2019). Visible Light Communications, IOP Publishing.","DOI":"10.1088\/2053-2563\/ab3eb0"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"46317","DOI":"10.1109\/ACCESS.2019.2909490","article-title":"Quantum machine learning for 6G communication networks: State-of-the-art and vision for the future","volume":"7","author":"Nawaz","year":"2019","journal-title":"IEEE Access"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Wang, Z., Liu, L., and Cui, S. (2020, January 25\u201328). Channel Estimation for Intelligent Reflecting Surface Assisted Multiuser Communications. Proceedings of the 2020 IEEE Wireless Communications and Networking Conference (WCNC), Seoul, Korea.","DOI":"10.1109\/WCNC45663.2020.9120452"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Tataria, H., Tufvesson, F., and Edfors, O. (2020, January 4\u20138). Real-Time Implementation Aspects of Large Intelligent Surfaces. Proceedings of the ICASSP 2020\u20142020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Barcelona, Spain.","DOI":"10.1109\/ICASSP40776.2020.9053897"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1447","DOI":"10.1109\/LWC.2020.2993699","article-title":"Deep Channel Learning For Large Intelligent Surfaces Aided mm-Wave Massive MIMO Systems","volume":"9","author":"Elbir","year":"2020","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"8902","DOI":"10.1109\/JIOT.2020.2996984","article-title":"Design, Analysis and Optimization of A Large Intelligent Reflecting Surface Aided B5G Cellular Internet of Things","volume":"7","author":"Yu","year":"2020","journal-title":"IEEE Internet Things J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5561","DOI":"10.1109\/TWC.2020.2994455","article-title":"Joint Reflecting and Precoding Designs for SER Minimization in Reconfigurable Intelligent Surfaces Assisted MIMO Systems","volume":"19","author":"Ye","year":"2020","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Yue, D.W., Nguyen, H.H., and Sun, Y. (2020). mmWave Doubly-Massive-MIMO Communications Enhanced with an Intelligent Reflecting Surface. arXiv.","DOI":"10.1109\/ACCESS.2020.3029244"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"He, J., Wymeersch, H., Kong, L., Silv\u00e9n, O., and Juntti, M. (2020, January 25\u201328). Large Intelligent Surface for Positioning in Millimeter Wave MIMO Systems. Proceedings of the 2020 IEEE 91st Vehicular Technology Conference (VTC2020-Spring), Antwerp, Belgium.","DOI":"10.1109\/VTC2020-Spring48590.2020.9129075"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2526","DOI":"10.1109\/JSAC.2020.3007036","article-title":"Communicating with Large Intelligent Surfaces: Fundamental Limits and Models","volume":"38","author":"Dardari","year":"2020","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2052","DOI":"10.1109\/TWC.2019.2961990","article-title":"Performance Analysis of Large Intelligent Surfaces (LISs): Asymptotic Data Rate and Channel Hardening Effects","volume":"19","author":"Jung","year":"2020","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1793","DOI":"10.1109\/JSAC.2020.3000811","article-title":"Passive Beamforming and Information Transfer Design for Reconfigurable Intelligent Surfaces Aided Multiuser MIMO Systems","volume":"38","author":"Yan","year":"2020","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1109\/LWC.2019.2947445","article-title":"Communication Through a Large Reflecting Surface With Phase Errors","volume":"9","author":"Badiu","year":"2020","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2043","DOI":"10.1109\/25.901862","article-title":"Single-user and multiuser adaptive maximal ratio transmission for Rayleigh channels","volume":"49","author":"Cavers","year":"2000","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Makarfi, A.U., Rabie, K.M., Kaiwartya, O., Li, X., and Kharel, R. (2020, January 25\u201328). Physical Layer Security in Vehicular Networks with Reconfigurable Intelligent Surfaces. Proceedings of the 2020 IEEE 91st Vehicular Technology Conference (VTC2020-Spring), Antwerp, Belgium.","DOI":"10.1109\/VTC2020-Spring48590.2020.9128438"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Qian, X., Di Renzo, M., Liu, J., Kammoun, A., and Alouini, M.S. (2020). Beamforming Through Reconfigurable Intelligent Surfaces in Single-User MIMO Systems: SNR Distribution and Scaling Laws in the Presence of Channel Fading and Phase Noise. arXiv.","DOI":"10.1109\/LWC.2020.3021058"},{"key":"ref_18","unstructured":"Bj\u00f6rnson, E., and Sanguinetti, L. (2020). Rayleigh Fading Modeling and Channel Hardening for Reconfigurable Intelligent Surfaces. arXiv."},{"key":"ref_19","unstructured":"Nadeem, Q.U.A., Kammoun, A., Chaaban, A., Debbah, M., and Alouini, M.S. (2019). Asymptotic Analysis of Large Intelligent Surface Assisted MIMO Communication. arXiv."},{"key":"ref_20","unstructured":"Papoulis, A., and Pillai, S.U. (2002). Probability, Random Variables, and Stochastic Processes, McGraw Hill. [4th ed.]."},{"key":"ref_21","unstructured":"Cover, T.M., and Thomas, J.A. (2006). Elements of Information Theory, Wiley-Interscience."},{"key":"ref_22","unstructured":"Proakis (2007). Digital Communications, McGraw Hill. [5th ed.]."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Goldsmith, A. (2005). Wireless Communications, Cambridge University Press.","DOI":"10.1017\/CBO9780511841224"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1109\/OJCOMS.2020.2996797","article-title":"Bit Error Probability for Large Intelligent Surfaces Under Double-Nakagami Fading Channels","volume":"1","author":"Ferreira","year":"2020","journal-title":"IEEE Open J. Commun. Soc."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/22\/6679\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:35:44Z","timestamp":1760178944000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/22\/6679"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,22]]},"references-count":24,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["s20226679"],"URL":"https:\/\/doi.org\/10.3390\/s20226679","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,11,22]]}}}