{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:21:42Z","timestamp":1760242902813,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2016,10,17]],"date-time":"2016-10-17T00:00:00Z","timestamp":1476662400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF-2014R1A1A1A05005551","NRF-2015R1D1A1A01057100"],"award-info":[{"award-number":["NRF-2014R1A1A1A05005551","NRF-2015R1D1A1A01057100"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we consider a transmit power allocation problem for secure transmission in multi-hop decode-and-forward (DF) full-duplex relay (FDR) networks, where multiple FDRs are located at each hop and perform cooperative beamforming to null out the signal at multiple eavesdroppers. For a perfect self-interference cancellation (PSIC) case, where the self-interference signal at each FDR is completely canceled, we derive an optimal power allocation (OPA) strategy using the Karush-Kuhn-Tucker (KKT) conditions to maximize the achievable secrecy rate under an overall transmit power constraint. In the case where residual self-interferences exist owing to imperfect self-interference cancellation (ISIC), we also propose a transmit power allocation scheme using the geometric programming (GP) method. Numerical results are presented to verify the secrecy rate performance of the proposed power allocation schemes.<\/jats:p>","DOI":"10.3390\/s16101726","type":"journal-article","created":{"date-parts":[[2016,10,17]],"date-time":"2016-10-17T10:33:16Z","timestamp":1476700396000},"page":"1726","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Transmit Power Allocation for Physical Layer Security in Cooperative Multi-Hop Full-Duplex Relay Networks"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7439-1740","authenticated-orcid":false,"given":"Jong-Ho","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Electronic Engineering, Gachon University, Seongnam 13120, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Illsoo","family":"Sohn","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Gachon University, Seongnam 13120, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2183-5085","authenticated-orcid":false,"given":"Yong-Hwa","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Myongji University, Yongin 17058, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,10,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1550","DOI":"10.1109\/SURV.2014.012314.00178","article-title":"Principles of physical layer security in multiuser wireless networks: A survey","volume":"16","author":"Mukherjee","year":"2014","journal-title":"IEEE Commun. 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