{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:16:32Z","timestamp":1760148992749,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2023,6,27]],"date-time":"2023-06-27T00:00:00Z","timestamp":1687824000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Federal District Research Foundation (Funda\u00e7\u00e3o de Apoio \u00e0 Pesquisa do Distrito Federal\u2014FAP\/DF), Brazil"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Due to the increase in the number of mobile stations in recent years, cooperative relaying systems have emerged as a promising technique for improving the quality of fifth-generation (5G) wireless networks with an extension of the coverage area. In this paper, we propose a two-hop orthogonal frequency division multiplexing and code-division multiple-access (OFDM-CDMA) multiple-input multiple-output (MIMO) relay system, which combines, both at the source and relay nodes, a tensor space\u2013time\u2013frequency (TSTF) coding with a multiple symbol matrices Kronecker product (MSMKron), called TSTF-MSMKron coding, aiming to increase the diversity gain. It is first established that the signals received at the relay and the destination satisfy generalized Tucker models whose core tensors are the coding tensors. Assuming the coding tensors are known at both nodes, tensor models are exploited to derive two semi-blind receivers, composed of two steps, to jointly estimate symbol matrices and individual channels. Necessary conditions for parameter identifiability with each receiver are established. Extensive Monte Carlo simulation results are provided to show the impact of design parameters on the symbol error rate (SER) performance, using the zero-forcing (ZF) receiver. Next, Monte Carlo simulations illustrate the effectiveness of the proposed TSTF-MSMKron coding and semi-blind receivers, highlighting the benefit of exploiting the new coding to increase the diversity gain.<\/jats:p>","DOI":"10.3390\/s23135963","type":"journal-article","created":{"date-parts":[[2023,6,28]],"date-time":"2023-06-28T00:45:11Z","timestamp":1687913111000},"page":"5963","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Semi-Blind Receivers for Two-Hop MIMO Relay Systems with a Combined TSTF-MSMKron Coding"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0390-5254","authenticated-orcid":false,"given":"Pablo H. U.","family":"de Pinho","sequence":"first","affiliation":[{"name":"University of Brasilia, Federal District, Brasilia 70910-900, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1256-0067","authenticated-orcid":false,"given":"Maria de F. K. B.","family":"Couras","sequence":"additional","affiliation":[{"name":"University of Brasilia, Federal District, Brasilia 70910-900, Brazil"},{"name":"I3S Laboratory, CNRS, Universit\u00e9 C\u00f4te d\u2019Azur, 06903 Sophia Antipolis, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8882-7410","authenticated-orcid":false,"given":"G\u00e9rard","family":"Favier","sequence":"additional","affiliation":[{"name":"I3S Laboratory, CNRS, Universit\u00e9 C\u00f4te d\u2019Azur, 06903 Sophia Antipolis, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3149-6307","authenticated-orcid":false,"given":"Andr\u00e9 L. F.","family":"de Almeida","sequence":"additional","affiliation":[{"name":"Federal University of Ceara, Fortaleza 60020-181, Ceara, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8616-4924","authenticated-orcid":false,"given":"Jo\u00e3o Paulo J.","family":"da Costa","sequence":"additional","affiliation":[{"name":"University of Brasilia, Federal District, Brasilia 70910-900, Brazil"},{"name":"Hamm-Lippstadt University of Applied Sciences, 59063 Hamm, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Goldsmith, A. (2005). Wireless Communications, Cambridge University Press.","DOI":"10.1017\/CBO9780511841224"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Chataut, R., and Akl, R. (2020). 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