{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:25:05Z","timestamp":1760239505183,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2020,11,12]],"date-time":"2020-11-12T00:00:00Z","timestamp":1605139200000},"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>In this paper, we consider a two-user downlink full-duplex (FD) non-orthogonal multiple access (NOMA) relay system where the FD relay uses an energy harvesting (EH) technique to assist the communication between the base station and far user over flat, independent and non-identically Rayleigh fading channels. Importantly, since the relay operates in FD mode, we take into account the effect of the interference caused by relay on the near user. Considering this EH-FD-NOMA relay system, we derive the exact mathematical expressions of the outage probabilities and ergodic capacities of near and far users. Monte\u2013Carlo simulations verify the accuracy of our analytical method. Numerical results provided in this paper allow system designers to clearly see not only the impacts of the power distribution factor and the self-interference cancellation capacity of the relay but also the influence of the strength of inter-user interference at the near user on the outage performances and ergodic capacities of both users.<\/jats:p>","DOI":"10.3390\/s20226472","type":"journal-article","created":{"date-parts":[[2020,11,12]],"date-time":"2020-11-12T20:17:52Z","timestamp":1605212272000},"page":"6472","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Outage Probability and Ergodic Capacity of a Two-User NOMA Relaying System with an Energy Harvesting Full-Duplex Relay and Its Interference at the Near User"],"prefix":"10.3390","volume":"20","author":[{"given":"Hoang Van","family":"Toan","sequence":"first","affiliation":[{"name":"Faculty of Telecommunications Services, Telecommunications University, Khanh Hoa 650000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tran Manh","family":"Hoang","sequence":"additional","affiliation":[{"name":"Faculty of Telecommunications Services, Telecommunications University, Khanh Hoa 650000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3947-2174","authenticated-orcid":false,"given":"Tran Trung","family":"Duy","sequence":"additional","affiliation":[{"name":"Department of Telecommunications, Posts and Telecommunications Institute of Technology, Ho Chi Minh 700000, 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 700000, Vietnam"},{"name":"Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh 700000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/MCOM.2014.6815890","article-title":"Scenarios for 5G mobile and wireless communications: The vision of the METIS project","volume":"52","author":"Osseiran","year":"2014","journal-title":"IEEE Commun. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"900","DOI":"10.1109\/TCCN.2019.2933835","article-title":"Interplay Between NOMA and Other Emerging Technologies: A Survey","volume":"5","author":"Vaezi","year":"2019","journal-title":"IEEE Trans. Cogn. Commun. Netw."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1049\/iet-com.2016.0742","article-title":"Robust resource allocation for orthogonal frequency division multiplexing-based cooperative cognitive radio networks with imperfect channel state information","volume":"11","author":"Yang","year":"2017","journal-title":"IET Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1109\/JSAC.2008.080402","article-title":"Multiuser detection of sparsely spread CDMA","volume":"26","author":"Guo","year":"2008","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1616","DOI":"10.1109\/TSP.2007.909320","article-title":"Novel low-density signature for synchronous CDMA systems over AWGN channel","volume":"56","author":"Hoshyar","year":"2008","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Hoang, T.M., Nguyen, B.C., and Tran, X.N. (2020). Outage Probability and Ergodic Capacity of User Clustering and Beamforming MIMO-NOMA Relay System with Imperfect CSI Over Nakagami-m Fading Channels. IEEE Syst. J.","DOI":"10.1109\/JSYST.2020.3009700"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1462","DOI":"10.1109\/LCOMM.2015.2441064","article-title":"Cooperative non-orthogonal multiple access in 5G systems","volume":"19","author":"Ding","year":"2015","journal-title":"IEEE Commun. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1606","DOI":"10.1109\/JSAC.2017.2699059","article-title":"Capacity analysis of NOMA with mmWave massive MIMO systems","volume":"35","author":"Zhang","year":"2017","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"6679","DOI":"10.1109\/TVT.2018.2805638","article-title":"When NOMA meets multiuser cognitive radio: Opportunistic cooperation and user scheduling","volume":"67","author":"Lv","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"8422","DOI":"10.1109\/TWC.2016.2614937","article-title":"Wireless-powered communications with non-orthogonal multiple access","volume":"15","author":"Diamantoulakis","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4296","DOI":"10.1109\/TWC.2012.102612.111278","article-title":"Experiment-driven characterization of full-duplex wireless systems","volume":"11","author":"Duarte","year":"2012","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"692","DOI":"10.1109\/LWC.2018.2811492","article-title":"On the coexistence between full-duplex and NOMA","volume":"7","author":"Ding","year":"2018","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2716","DOI":"10.1109\/TCOMM.2018.2890264","article-title":"Exploiting full-duplex two-way relay cooperative non-orthogonal multiple access","volume":"67","author":"Wang","year":"2018","journal-title":"IEEE Trans. Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"5574","DOI":"10.1109\/TCOMM.2019.2914210","article-title":"Secrecy analysis for cooperative NOMA networks with multi-antenna full-duplex relay","volume":"67","author":"Cao","year":"2019","journal-title":"IEEE Trans. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"5952","DOI":"10.1109\/TCOMM.2018.2858811","article-title":"Beamforming design and power allocation for full-duplex non-orthogonal multiple access cognitive relaying","volume":"66","author":"Mohammadi","year":"2018","journal-title":"IEEE Trans. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1109\/MCOM.2019.1800578","article-title":"Full-duplex non-orthogonal multiple access for next generation wireless systems","volume":"57","author":"Mohammadi","year":"2019","journal-title":"IEEE Commun. Mag."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2220","DOI":"10.1109\/TCOMM.2017.2665488","article-title":"Spectral and Energy Efficiencies in Full-Duplex Wireless Information and Power Transfer","volume":"65","author":"Nguyen","year":"2017","journal-title":"IEEE Trans. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2785","DOI":"10.1109\/TVT.2020.2964809","article-title":"Outage Analysis of RF Energy Harvesting Cooperative Communication Systems Over Nakagami-m Fading Channels With Integer and Non-Integer m","volume":"69","author":"Hoang","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"7286","DOI":"10.1109\/TVT.2017.2662641","article-title":"Asymptotically Optimal Power Allocation for Energy Harvesting Communication Networks","volume":"66","author":"Zlatanov","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1049\/iet-spr.2019.0612","article-title":"Analysing outage probability of linear and non-linear RF energy harvesting of cooperative communication networks","volume":"14","author":"Duong","year":"2020","journal-title":"IET Signal Proc."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"630","DOI":"10.1007\/s11036-018-1163-3","article-title":"Performance analysis of MIMO SWIPT relay network with imperfect CSI","volume":"24","author":"Hoang","year":"2019","journal-title":"Mob. Netw. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"152957","DOI":"10.1016\/j.aeue.2019.152957","article-title":"Outage probability of NOMA system with wireless power transfer at source and full-duplex relay","volume":"116","author":"Nguyen","year":"2020","journal-title":"AEU-Int. J. Electron. Commun."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"67057","DOI":"10.1109\/ACCESS.2018.2876859","article-title":"Full-duplex user relaying for NOMA system with self-energy recycling","volume":"6","author":"Wang","year":"2018","journal-title":"IEEE Access"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"5753","DOI":"10.1109\/TCOMM.2019.2914386","article-title":"Energy efficiency optimization in full-duplex user-aided cooperative SWIPT NOMA systems","volume":"67","author":"Yuan","year":"2019","journal-title":"IEEE Trans. Commun."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"804","DOI":"10.1109\/TGCN.2020.2977611","article-title":"SWIPT-enabled Full-Duplex NOMA Networks with Full and Partial CSI","volume":"4","author":"Liu","year":"2020","journal-title":"IEEE Trans. Green Commun. Netw."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"20442","DOI":"10.1109\/ACCESS.2019.2896252","article-title":"Energy Efficiency Maximization Design for Full-Duplex Cooperative NOMA Systems with SWIPT","volume":"7","author":"Huang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"7179","DOI":"10.1109\/TVT.2019.2914508","article-title":"Energy harvesting enabled NOMA systems with full-duplex relaying","volume":"68","author":"Guo","year":"2019","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"82442","DOI":"10.1109\/ACCESS.2020.2991847","article-title":"Joint Relay Selection, Full-Duplex and Device-to-Device Transmission in Wireless Powered NOMA Networks","volume":"8","author":"Dang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1109\/JCN.2018.000004","article-title":"Full-duplex distributed switch-and-stay energy harvesting selection relaying networks with imperfect CSI: Design and outage analysis","volume":"20","author":"Le","year":"2018","journal-title":"J. Commun. Netw."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3447","DOI":"10.1109\/TCOMM.2014.2357423","article-title":"Wireless Information and Power Transfer With Full Duplex Relaying","volume":"62","author":"Zhong","year":"2014","journal-title":"IEEE Trans. Commun."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"8466","DOI":"10.1109\/TVT.2018.2848963","article-title":"Resource allocation in SWIPT networks under a nonlinear energy harvesting model: Power efficiency, user fairness, and channel nonreciprocity","volume":"67","author":"Tran","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"12079","DOI":"10.1109\/TVT.2019.2948792","article-title":"Resource allocation for wireless-powered full-duplex relaying systems with nonlinear energy harvesting efficiency","volume":"68","author":"Wei","year":"2019","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3074","DOI":"10.1109\/TWC.2011.071411.102266","article-title":"Hybrid Full-Duplex\/Half-Duplex Relaying with Transmit Power Adaptation","volume":"10","author":"Riihonen","year":"2011","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1766","DOI":"10.1109\/LSP.2015.2432741","article-title":"Exploiting the direct link in full-duplex amplify-and-forward relaying networks","volume":"22","author":"Osorio","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"4970","DOI":"10.1109\/TWC.2017.2704123","article-title":"Channel Estimation for Residual Self-Interference in Full-Duplex Amplify-and-Forward Two-Way Relays","volume":"16","author":"Li","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2478","DOI":"10.1109\/LCOMM.2016.2611500","article-title":"Non-Orthogonal Multiple Access With Cooperative Full-Duplex Relaying","volume":"20","author":"Zhong","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_37","unstructured":"Gradshteyn, I.S., and Ryzhik, I.M. (2014). Table of Integrals, Series, and Products, Academic Press."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1316","DOI":"10.1109\/JSYST.2018.2850944","article-title":"Power splitting-based SWIPT with dual-hop DF relaying in the presence of a direct link","volume":"13","author":"Ye","year":"2018","journal-title":"IEEE Syst. J."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2354","DOI":"10.1109\/TVT.2012.2192488","article-title":"An efficient relay\u2013destination selection scheme for multiuser multirelay downlink cooperative networks","volume":"61","year":"2012","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_40","first-page":"415","article-title":"Relay-assisted diversity communications","volume":"62","author":"Tralli","year":"2012","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Bharadia, D., McMilin, E., and Katti, S. (2013, January 12\u201316). Full duplex radios. Proceedings of the ACM SIGCOMM 2013 Conference on SIGCOMM, Hong Kong, China.","DOI":"10.1145\/2486001.2486033"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/22\/6472\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:32:44Z","timestamp":1760178764000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/22\/6472"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,12]]},"references-count":41,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["s20226472"],"URL":"https:\/\/doi.org\/10.3390\/s20226472","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,11,12]]}}}