{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,3]],"date-time":"2026-01-03T06:44:04Z","timestamp":1767422644311,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,5,28]],"date-time":"2022-05-28T00:00:00Z","timestamp":1653696000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Fundamental Research Funds for the Central Universities","award":["2022JBGP003","62071033"],"award-info":[{"award-number":["2022JBGP003","62071033"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China (NSFC)","doi-asserted-by":"publisher","award":["2022JBGP003","62071033"],"award-info":[{"award-number":["2022JBGP003","62071033"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper investigates the outage performance of simultaneous wireless information and power transfer (SWIPT)-enabled relay networks with the decode-and-forward relaying protocol, where the effect of the energy triggering threshold at the relay on the system performance is considered. The closed-form expressions of the system outage probability and throughput are derived in Rician channel fading. Monte Carlo Simulation method is used to verify the accuracy of the derived closed-form expressions. The effects of some system parameters on the system performances are discussed via simulations, which show that the system outage probability increases with the increase of the minimum transmission rate required by the users and also decreases with the increase of the energy conversion efficiency. Besides, the system throughput increaseswith the increment of the transmit power of the source node, as well as the energy conversion efficiency. Additionally, the outage performance of the system with the equal two-hop distance is better than that of the system with unequal two-hop distance.<\/jats:p>","DOI":"10.3390\/e24060763","type":"journal-article","created":{"date-parts":[[2022,5,29]],"date-time":"2022-05-29T08:50:51Z","timestamp":1653814251000},"page":"763","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Outage Performance of Wireless Powered Decode-and-Forward Relaying Networks in Rician Fading"],"prefix":"10.3390","volume":"24","author":[{"given":"Zhifei","family":"Zhang","sequence":"first","affiliation":[{"name":"Engineering Research Center of Network Management Technology for High Speed Railway of Ministry of Education, School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Dong","sequence":"additional","affiliation":[{"name":"SinoRail HongYuan Software Technology Co., Ltd., Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinlu","family":"Tan","sequence":"additional","affiliation":[{"name":"Engineering Research Center of Network Management Technology for High Speed Railway of Ministry of Education, School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yaping","family":"Li","sequence":"additional","affiliation":[{"name":"Engineering Research Center of Network Management Technology for High Speed Railway of Ministry of Education, School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9364-0207","authenticated-orcid":false,"given":"Ke","family":"Xiong","sequence":"additional","affiliation":[{"name":"Engineering Research Center of Network Management Technology for High Speed Railway of Ministry of Education, School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1384","DOI":"10.1109\/COMST.2015.2497324","article-title":"Advances in Energy Harvesting Communications: Past, Present, and Future Challenges","volume":"18","author":"Ku","year":"2016","journal-title":"IEEE Commun. Surv. Tutorials"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"8899314:1","DOI":"10.1155\/2020\/8899314","article-title":"AN-Aided Secure Beamforming in SWIPT-Aware Mobile Edge Computing Systems with Cognitive Radio","volume":"2020","author":"Wang","year":"2020","journal-title":"Wirel. Commun. Mob. Comput."},{"key":"ref_3","unstructured":"Kschischang, F.R., and Yang, E. (2008, January 6\u201311). Transporting information and energy simultaneously. Proceedings of the International Symposium on Information Theory ISIT, Toronto, ON, Canada."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1989","DOI":"10.1109\/TWC.2013.031813.120224","article-title":"MIMO Broadcasting for Simultaneous Wireless Information and Power Transfer","volume":"12","author":"Zhang","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7906957:1","DOI":"10.1155\/2018\/7906957","article-title":"Power-Splitting Scheme for Nonlinear Energy Harvesting AF Relaying with Direct Link","volume":"2018","author":"Bai","year":"2018","journal-title":"Wirel. Commun. Mob. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3840","DOI":"10.1109\/TWC.2017.2689011","article-title":"Group Cooperation with Optimal Resource Allocation in Wireless Powered Communication Networks","volume":"16","author":"Xiong","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"7693016","DOI":"10.1155\/2018\/7693016","article-title":"Adaptive Energy Harvesting Relaying Protocol for Two-Way Half-Duplex System Network over Rician Fading Channels","volume":"2018","author":"Nguyen","year":"2018","journal-title":"Wirel. Commun. Mob. Comput."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1109\/TWC.2013.112513.130760","article-title":"Throughput Maximization in Wireless Powered Communication Networks","volume":"13","author":"Ju","year":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1839256:1","DOI":"10.1155\/2019\/1839256","article-title":"Joint Relay Selection and Power Allocation for the Physical Layer Security of Two-Way Cooperative Relaying Networks","volume":"2019","author":"Pan","year":"2019","journal-title":"Wirel. Commun. Mob. Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1206","DOI":"10.1109\/JSYST.2019.2940490","article-title":"Outage Probability and Throughput of Multirelay SWIPT-WPCN Networks With Nonlinear EH Model and Imperfect CSI","volume":"14","author":"Jiang","year":"2020","journal-title":"IEEE Syst. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5147","DOI":"10.1109\/TWC.2017.2706277","article-title":"Rate-Energy Region of SWIPT for MIMO Broadcasting Under Nonlinear Energy Harvesting Model","volume":"16","author":"Xiong","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1109\/LCOMM.2016.2627055","article-title":"Outage Probability Analysis and Power Splitter Designs for SWIPT Relaying Systems With Direct Link","volume":"21","author":"Lee","year":"2017","journal-title":"IEEE Commun. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1474","DOI":"10.1109\/LWC.2021.3070429","article-title":"Secrecy Outage Performance Analysis of Cooperative NOMA Networks with SWIPT","volume":"10","author":"Lei","year":"2021","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Liu, Z., Lu, G., Ye, Y., and Shi, L. (2020). On the Performance of Battery-Assisted PS-SWIPT Enabled DF Relaying. Information, 11.","DOI":"10.3390\/info11030165"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Tang, K., and Liao, S. (2020). Outage Analysis of Relay-Assisted NOMA in Cooperative Cognitive Radio Networks with SWIPT. Information, 11.","DOI":"10.3390\/info11110500"},{"key":"ref_16","first-page":"2516035:1","article-title":"Outage Analysis and Optimization of SWIPT in Network-Coded Two-Way Relay Networks","volume":"2017","author":"Jiang","year":"2017","journal-title":"Mob. Inf. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Xia, H., Li, Y., and Lu, Y. (2020). Relay Selection Optimization for SWIPT-Enabled Cooperative Networks. Information, 11.","DOI":"10.3390\/info11010007"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Guo, W., and Wang, Y. (2017). Cooperative Non-Orthogonal Multiple Access with Energy Harvesting. Information, 8.","DOI":"10.3390\/info8030111"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Soliman, S.S., and Beaulieu, N.C. (2013, January 28\u201331). Dual-hop AF systems with maximum end-to-end SNR relay selection over nakagami-m and rician fading links. Proceedings of the IEEE International Conference on Computing, Networking and Communications (ICNC), San Diego, CA, USA.","DOI":"10.1109\/ICCNC.2013.6504072"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1186\/s13638-017-1006-0","article-title":"Outage probability of power splitting SWIPT two-way relay networks in Nakagami-m fading","volume":"2018","author":"Zhong","year":"2018","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"13532","DOI":"10.1109\/TVT.2020.3030134","article-title":"System Outage Probability of PS-SWIPT Enabled Two-Way AF Relaying with Hardware Impairments","volume":"69","author":"Liu","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1186\/s13638-018-1050-4","article-title":"Performance analysis of energy-harvesting-aware multi-relay networks in Nakagami-m fading","volume":"2018","author":"Zhong","year":"2018","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"6384","DOI":"10.1109\/TCOMM.2018.2865944","article-title":"Secrecy Outage Analysis of Mixed RF-FSO Downlink SWIPT Systems","volume":"66","author":"Lei","year":"2018","journal-title":"IEEE Trans. Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"10167","DOI":"10.1109\/TVT.2020.3003228","article-title":"On Outage Analysis in SWIPT Enabled Bidirectional D2D Communications Using Spectrum Sharing in Cellular Networks","volume":"69","author":"Ghosh","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/LSENS.2019.2928024","article-title":"Performance of Wireless Powered Cognitive Radio Sensor Networks with Nonlinear Energy Harvester","volume":"3","author":"Gurjar","year":"2019","journal-title":"IEEE Sens. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"13467","DOI":"10.1109\/TVT.2020.3029067","article-title":"Performance Analysis and Optimization of Bidirectional Overlay Cognitive Radio Networks with Hybrid-SWIPT","volume":"69","author":"Prathima","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2703","DOI":"10.1002\/dac.2500","article-title":"Performance analysis of cooperative network over Nakagami and Rician fading channels","volume":"27","author":"Khan","year":"2014","journal-title":"Int. J. Commun. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1109\/TCOMM.2015.2506699","article-title":"Joint Optimization Schemes for Cooperative Wireless Information and Power Transfer over Rician Channels","volume":"64","author":"Mishra","year":"2016","journal-title":"IEEE Trans. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Sheng, X., Lu, G., Shi, L., and Ye, Y. (2019). Performance Analysis of Hybrid Protocol Based AF EH Relaying over Asymmetric Fading Channels. Information, 10.","DOI":"10.3390\/info10020050"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Jameel, F., Jayakody, D.N.K., Flanagan, M.F., and Tellambura, C. (2018, January 15\u201318). Secure communication for separated and integrated receiver architectures in SWIPT. Proceedings of the IEEE Wireless Communications and Networking Conference (WCNC), Barcelona, Spain.","DOI":"10.1109\/WCNC.2018.8377127"},{"key":"ref_31","first-page":"1595","article-title":"Wireless Information and Energy Transfer for Two-Hop Non-Regenerative MIMO-OFDM Relay Networks","volume":"33","author":"Xiong","year":"2015","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_32","unstructured":"Lee, J.B., Rong, Y., Gopal, L., and Chiong, C.W.R. (2021). Robust Transceiver Design for SWIPT DF MIMO Relay Systems with Time-Switching Protocol. IEEE Syst. J., 1\u201312."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Wu, M., Song, Q., Ni, Q., Guo, L., Ning, Z., and Obaidat, M.S. (2021, January 14\u201323). Joint User Pairing and Resource Allocation for SWIPT-Enabled Cooperative D2D Communications. Proceedings of the IEEE International Conference on Communications, Montreal, QC, Canada.","DOI":"10.1109\/ICC42927.2021.9500598"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1109\/TCOMM.2021.3120714","article-title":"Relay-Aided Multi-User OFDM Relying on Joint Wireless Power Transfer and Self-Interference Recycling","volume":"70","author":"Nasir","year":"2022","journal-title":"IEEE Trans. Commun."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1109\/TCCN.2019.2960217","article-title":"On Residual Energy Maximization in DF Cognitive Radio Networks with Multiple Eavesdroppers","volume":"6","author":"Banerjee","year":"2020","journal-title":"IEEE Trans. Cogn. Commun. Netw."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"628","DOI":"10.1109\/LWC.2018.2890605","article-title":"Average Age of Information in Wireless Powered Sensor Networks","volume":"8","author":"Krikidis","year":"2019","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1859","DOI":"10.1007\/s11277-018-5885-0","article-title":"Performance of TAS\/MRC Wireless Energy Harvesting Relaying Networks over Rician Fading Channels","volume":"103","author":"Anh","year":"2018","journal-title":"Wirel. Pers. Commun."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_39","unstructured":"Gradshteyn, I.S., and Ryzhik, I.M. (2007). Table of Integrals, Series, and Products, Elsevier\/Academic Press. [7th ed.]."},{"key":"ref_40","unstructured":"Guo, J., and Zhu, X. (2012, January 17\u201322). An improved analytical model for RF-DC conversion efficiency in microwave rectifiers. Proceedings of the 2012 IEEE\/MTT-S International Microwave Symposium Digest, Montreal, QC, Canada."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"7245","DOI":"10.1109\/TCOMM.2019.2928542","article-title":"Alcaraz L\u00f3pez and Hirley Alves and Richard Demo Souza and Samuel Montejo S\u00e1nchez. Statistical Analysis of Multiple Antenna Strategies for Wireless Energy Transfer","volume":"67","author":"Onel","year":"2019","journal-title":"IEEE Trans. Commun."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/6\/763\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:20:39Z","timestamp":1760138439000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/6\/763"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,28]]},"references-count":41,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["e24060763"],"URL":"https:\/\/doi.org\/10.3390\/e24060763","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,5,28]]}}}