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Beams are grouped in clusters managed by different non-cooperative gateways. A two-level approach is performed, with an on-board beamforming network complemented by on-ground precoders. The former, designed with the SLNR (signal-to-leakage and noise ratio) criterion, mitigates the inter-cluster interference, whereas the latter fight the intra-cluster multiuser co-channel interference. Judicious user scheduling is also addressed to limit the impact of the multicasting and limited adaptation capabilities. Several two-level precoding designs can be obtained by setting accordingly the degree of cooperation and the frame adaptation, with an overall satisfactory performance with respect to the single-gateway benchmark. In particular, a sector-based solution with non-cooperative gateways presents a good trade-off between gateway autonomy and performance.<\/jats:p>","DOI":"10.1186\/s13638-020-01757-7","type":"journal-article","created":{"date-parts":[[2020,7,20]],"date-time":"2020-07-20T11:03:32Z","timestamp":1595243012000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Two-level frame precoding with non-cooperative gateways"],"prefix":"10.1186","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2300-2741","authenticated-orcid":false,"given":"Tom\u00e1s","family":"Ram\u00edrez","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carlos","family":"Mosquera","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roberto","family":"L\u00f3pez-Valcarce","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,7,20]]},"reference":[{"key":"1757_CR1","doi-asserted-by":"publisher","DOI":"10.1002\/9781118984086","volume-title":"Innovations in Satellite Communications Technology","author":"D. 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