{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T13:38:29Z","timestamp":1761745109264,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2019,12,6]],"date-time":"2019-12-06T00:00:00Z","timestamp":1575590400000},"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>Full-duplex (FD) communication and spatial modulation (SM) are two promising techniques to achieve high spectral efficiency. Recent works in the literature have investigated the possibility of combining the FD mode with SM in the relay system to benefit their advantages. In this paper, we analyze the performance of the FD-SM decode-and-forward (DF) relay system and derive the closed-form expression for the symbol error probability (SEP). To tackle the residual self-interference (RSI) due to the FD mode at the relay, we propose a simple yet effective power allocation algorithm to compensate for the RSI impact and improve the system SEP performance. Both numerical and simulation results confirm the accuracy of the derived SEP expression and the efficacy of the proposed optimal power allocation.<\/jats:p>","DOI":"10.3390\/s19245390","type":"journal-article","created":{"date-parts":[[2019,12,6]],"date-time":"2019-12-06T10:41:44Z","timestamp":1575628904000},"page":"5390","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Closed-Form Expression for the Symbol Error Probability in Full-Duplex Spatial Modulation Relay System and Its Application in Optimal Power Allocation"],"prefix":"10.3390","volume":"19","author":[{"given":"Le Van","family":"Nguyen","sequence":"first","affiliation":[{"name":"Advanced Wireless Communications Group, Le Quy Don Technical University, Hanoi 11917, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4532-5493","authenticated-orcid":false,"given":"Ba Cao","family":"Nguyen","sequence":"additional","affiliation":[{"name":"Advanced Wireless Communications Group, Le Quy Don Technical University, Hanoi 11917, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuan Nam","family":"Tran","sequence":"additional","affiliation":[{"name":"Advanced Wireless Communications Group, Le Quy Don Technical University, Hanoi 11917, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7297-7705","authenticated-orcid":false,"given":"Le The","family":"Dung","sequence":"additional","affiliation":[{"name":"Division of Computational Physics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam"},{"name":"Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1109\/LWC.2014.2359218","article-title":"Spatial modulated full duplex","volume":"3","author":"Jiao","year":"2014","journal-title":"IEEE Wirel. 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