{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T15:40:35Z","timestamp":1783611635674,"version":"3.55.0"},"reference-count":44,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2020,8,21]],"date-time":"2020-08-21T00:00:00Z","timestamp":1597968000000},"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>A downlink of multi-user non-orthogonal multiple access (NOMA) relay systems is considered. To improve system performance, relay nodes are used to forward signals from the base station (BS) to the end users, and they are wirelessly powered by energy harvesting from the radio frequency transmitted from the BS. Moreover, beamforming is applied at the BS based on multiple antennas and relay nodes consist of one transmit antenna but several receive ones. The system performance is demonstrated through closed-form expressions of outage probability (OP) and ergodic rate (ER) over Rayleigh fading channels. The proposed system is investigated in two cases of perfect and imperfect successive interference cancellation (SIC), and the imperfect channel state information condition is also taken into consideration. The OP and ER are calculated in many scenarios and the optimal time fraction of energy harvesting corresponding to the minimum OP is discussed. The exact and approximate theoretical results are compared with the simulation result to confirm the proposed theoretical analysis method.<\/jats:p>","DOI":"10.3390\/s20174737","type":"journal-article","created":{"date-parts":[[2020,8,21]],"date-time":"2020-08-21T09:21:51Z","timestamp":1598001711000},"page":"4737","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["On Outage Probability and Ergodic Rate of Downlink Multi-User Relay Systems with Combination of NOMA, SWIPT, and Beamforming"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6117-2100","authenticated-orcid":false,"given":"Ta","family":"Chi Hieu","sequence":"first","affiliation":[{"name":"Faculty of Radio-Electronic Engineering, Le Quy Don Technical University, 236 Hoang Quoc Viet, Hanoi 100000, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nguyen","family":"Le Cuong","sequence":"additional","affiliation":[{"name":"Faculty of Electronics and Telecommunications, Electric Power University, 238 Hoang Quoc Viet, Hanoi 100000, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3393-207X","authenticated-orcid":false,"given":"Tran","family":"Manh Hoang","sequence":"additional","affiliation":[{"name":"Faculty of Profesional Telecommunications, Nha trang University of Telecommunication, 101 Mai Xuan Thuong, Nha Trang 650000, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Do","family":"Thanh Quan","sequence":"additional","affiliation":[{"name":"Faculty of Radio-Electronic Engineering, Le Quy Don Technical University, 236 Hoang Quoc Viet, Hanoi 100000, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8288-6436","authenticated-orcid":false,"given":"Pham","family":"Thanh Hiep","sequence":"additional","affiliation":[{"name":"Faculty of Radio-Electronic Engineering, Le Quy Don Technical University, 236 Hoang Quoc Viet, Hanoi 100000, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2722","DOI":"10.1109\/JSEN.2019.2951345","article-title":"WaterGrid-Sense: A LoRa-Based Sensor Node for Industrial IoT Applications","volume":"20","author":"Khutsoane","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"8182","DOI":"10.1109\/JIOT.2019.2935189","article-title":"IoT: Internet of Threats? A Survey of Practical Security Vulnerabilities in Real IoT Devices","volume":"6","author":"Meneghello","year":"2019","journal-title":"IEEE Internet Things J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"9036","DOI":"10.1109\/JSEN.2019.2922409","article-title":"Sensing, Controlling, and IoT Infrastructure in Smart Building: A Review","volume":"19","author":"Verma","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/JIOT.2019.2948888","article-title":"A Comprehensive Survey on Internet of Things (IoT) toward 5G Wireless Systems","volume":"7","author":"Chettri","year":"2020","journal-title":"IEEE Internet Things J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1109\/MCOM.2018.1701310","article-title":"From IoT to 5G I-IoT: The Next Generation IoT-Based Intelligent Algorithms and 5G Technologies","volume":"56","author":"Wang","year":"2018","journal-title":"IEEE Commun. Mag."},{"key":"ref_6","first-page":"2347","article-title":"Non orthogonal Multiple Access for 5G and Beyond","volume":"105","author":"Liu","year":"2017","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2667","DOI":"10.1109\/JSAC.2017.2726718","article-title":"Non-orthogonal multiple access in large-scale heterogeneous networks","volume":"35","author":"Liu","year":"2017","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"7828","DOI":"10.1109\/JIOT.2019.2908415","article-title":"Cooperative NOMA Broadcasting\/Multicasting for Low-Latency and High-Reliability 5G Cellular V2X Communications","volume":"6","author":"Liu","year":"2019","journal-title":"IEEE Internet Things J."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Vamvakas, P., Tsiropoulou, E.E., and Papavassiliou, S. (2019, January 10\u201312). Risk-aware resource control with flexible 5G access technology interfaces. Proceedings of the 2019 IEEE 20th International Symposium on \u201cA World of Wireless, Mobile and Multimedia Networks\u201d (WoWMoM), Washington, DC, USA.","DOI":"10.1109\/WoWMoM.2019.8792980"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2860","DOI":"10.1109\/JSAC.2017.2726218","article-title":"Resource optimization and power allocation in in-band full duplex-enabled non-orthogonal multiple access networks","volume":"35","author":"Elbamby","year":"2017","journal-title":"IEEE J. Sel. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1109\/TCOMM.2015.2394393","article-title":"Minimum power multicast beamforming with superposition coding for multiresolution broadcast and application to NOMA systems","volume":"63","author":"Choi","year":"2015","journal-title":"IEEE Trans. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1049\/iet-com.2016.0428","article-title":"Energy-efficient optimisation for secrecy wireless information and power transfer in massive MIMO relaying systems","volume":"11","author":"Du","year":"2016","journal-title":"IET Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1947","DOI":"10.1049\/iet-com.2016.0120","article-title":"Transceiver Design for Cooperative Non-Orthogonal Multiple Access Systems with Wireless Energy Transfer","volume":"10","author":"Sun","year":"2016","journal-title":"IET Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2687","DOI":"10.1049\/iet-com.2016.0630","article-title":"Performance Analysis for NOMA Energy Harvesting Relaying Networks with Transmit Antenna Selection and Maximal-Ratio Combining over Nakagami-m Fading","volume":"10","author":"Han","year":"2016","journal-title":"IET Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"938","DOI":"10.1109\/JSAC.2016.2549378","article-title":"Cooperative non-orthogonal multiple access with simultaneous wireless information and power transfer","volume":"34","author":"Liu","year":"2016","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_16","unstructured":"Perera, T.D.P., Jayakody, D.N.K., Sharma, S.K., Chatzinotas, S., and Li, J. (2017). Simultaneous Wireless Information and Power Transfer (SWIPT): Recent Advances and Future Challenges. IEEE Commun. Surv. Tutor."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Hoang, T.M., Duy, T.T., and Bao, V.N.Q. (2016, January 14\u201316). On the performance of non-linear wirelessly powered partial relay selection networks over Rayleigh fading channels. Proceedings of the 2016 3rd National Foundation for Science and Technology Development Conference on Information and Computer Science (NICS 2016), Danang City, Vietnam.","DOI":"10.1109\/NICS.2016.7725668"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1109\/TCOMM.2012.102512.110679","article-title":"Outage probability of dual-hop multiple antenna AF relaying systems with interference","volume":"61","author":"Zhong","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1769","DOI":"10.1109\/TCOMM.2016.2527785","article-title":"Throughput Analysis and Optimization of Wireless-Powered Multiple Antenna Full-Duplex Relay Systems","volume":"64","author":"Mohammadi","year":"2016","journal-title":"IEEE Trans. Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1400","DOI":"10.1109\/TCOMM.2015.2398862","article-title":"Wireless information and power transfer in relay systems with multiple antennas and interference","volume":"63","author":"Zhu","year":"2015","journal-title":"IEEE Trans. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.phycom.2018.03.016","article-title":"Design of incentive scheme using contract theory in energy-harvesting enabled sensor networks","volume":"28","author":"Gui","year":"2018","journal-title":"Phys. Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2976","DOI":"10.1109\/TWC.2017.2672964","article-title":"Online ski rental for on\/off scheduling of energy harvesting base stations","volume":"16","author":"Lee","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Vamvakas, P., Tsiropoulou, E.E., Vomvas, M., and Papavassiliou, S. (2017, January 18\u201320). Adaptive power management in wireless powered communication networks: A user-centric approach. Proceedings of the 2017 IEEE 38th Sarnoff Symposium, Newark, NJ, USA.","DOI":"10.1109\/SARNOF.2017.8080386"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1109\/TWC.2013.010213.130484","article-title":"Power allocation strategies in energy harvesting wireless cooperative networks","volume":"13","author":"Ding","year":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_25","first-page":"902","article-title":"Enabling wireless power transfer in cellular networks: Architecture, modeling and deployment","volume":"13","author":"Huang","year":"2014","journal-title":"IEEE Trans. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1109\/LCOMM.2016.2547985","article-title":"Outage performance of underlay multihop cognitive relay networks with energy harvesting","volume":"20","author":"Xu","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1109\/TCOMM.2015.2498171","article-title":"Secure D2D communication in large-scale cognitive cellular networks: A wireless power transfer model","volume":"64","author":"Liu","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"5178","DOI":"10.1109\/TCOMM.2015.2488640","article-title":"Wireless-powered communications: Performance analysis and optimization","volume":"63","author":"Zhong","year":"2015","journal-title":"IEEE Trans. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3569","DOI":"10.1109\/TCOMM.2015.2468215","article-title":"Distributed and optimal resource allocation for power beacon-assisted wireless-powered communications","volume":"63","author":"Ma","year":"2015","journal-title":"IEEE Trans. Commun."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Vinh, H.D., Van Son, V., Hoang, T.M., Hieu, T.C., and Hiep, P.T. (2019, January 24\u201326). Performance Analysis of NOMA Beamforming Multiple Users Relay Systems. Proceedings of the 2019 11th International Conference on Knowledge and Systems Engineering (KSE), Da Nang, Vietnam.","DOI":"10.1109\/KSE.2019.8919322"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.icte.2019.05.004","article-title":"Non-orthogonal multiple access and beamforming for relay network with RF energy harvesting","volume":"6","author":"Hiep","year":"2020","journal-title":"ICT Express"},{"key":"ref_32","unstructured":"Zwillinger, D. (2014). Table of Integrals, Series, and Products, Elsevier."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2562","DOI":"10.1109\/TIT.2003.817433","article-title":"On beamforming with finite rate feedback in multiple-antenna systems","volume":"49","author":"Mukkavilli","year":"2003","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Singhal, C., and De, S. (2017). Resource Allocation in Next-Generation Broadband Wireless Access Networks, IGI Global.","DOI":"10.4018\/978-1-5225-2023-8"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3282","DOI":"10.1109\/TWC.2017.2679055","article-title":"MIMO energy harvesting in full-duplex multi-user networks","volume":"16","author":"Tam","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"3622","DOI":"10.1109\/TWC.2013.062413.122042","article-title":"Relaying protocols for wireless energy harvesting and information processing","volume":"12","author":"Nasir","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"4754","DOI":"10.1109\/TCOMM.2013.13.120855","article-title":"Wireless information and power transfer: Architecture design and rate-energy tradeoff","volume":"61","author":"Zhou","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2563","DOI":"10.1109\/TIT.2014.2311822","article-title":"Capacity of Gaussian channels with energy harvesting and processing cost","volume":"60","author":"Rajesh","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Shankar, P.M. (2017). Fading and Shadowing in Wireless Systems, Springer.","DOI":"10.1007\/978-3-319-53198-4"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Miller, S., and Childers, D. (2012). Probability and Random Processes: With Applications to Signal Processing and Communications, Academic Press.","DOI":"10.1016\/B978-0-12-386981-4.50011-4"},{"key":"ref_41","unstructured":"Papoulis, A., and Pillai, S.U. (2002). Probability, Random Variables, and Stochastic Processes, Tata McGraw-Hill Education."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"4585","DOI":"10.1007\/s11276-018-1746-8","article-title":"Performance analysis of decode-and-forward partial relay selection in NOMA systems with RF energy harvesting","volume":"25","author":"Hoang","year":"2019","journal-title":"Wirel. Netw."},{"key":"ref_43","unstructured":"Abramowitz, M., and Stegun, I.A. (1964). Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables, Courier Corporation."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1381","DOI":"10.1109\/LCOMM.2017.2666152","article-title":"Optimization of cognitive two-way networks with energy harvesting relays","volume":"21","author":"Singh","year":"2017","journal-title":"IEEE Commun. Lett."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/17\/4737\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:04:52Z","timestamp":1760177092000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/17\/4737"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,21]]},"references-count":44,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2020,9]]}},"alternative-id":["s20174737"],"URL":"https:\/\/doi.org\/10.3390\/s20174737","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,21]]}}}