{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:46:45Z","timestamp":1760240805573,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2019,9,20]],"date-time":"2019-09-20T00:00:00Z","timestamp":1568937600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Future Internet"],"abstract":"<jats:p>In this paper, we propose an optimal time and power allocation scheme in a wireless power supply full-duplex (FD) relay system, where we consider the number of relay antennas in the energy harvesting stage. At the same time, the energy efficiency optimization problem of the system is structured, where optimization issues related to time allocation factors and power allocation are established. For the FD dual-antenna and the FD single-antenna energy harvesting system, energy efficiency function is proven to be a concave function over the time-switch factor, and the optimal time-switching factor is theoretically obtained using the Lambert function. Then, according to the given value range of the optimal time switching factor, the optimal power distribution scheme is obtained by analyzing the derivative function of the system energy efficiency and using the properties of the Lambert function. The time-switching factor and transmission power are optimally selected at the wireless power supply FD relay. Results reveal that the performance of energy efficiency of the dual-antenna energy harvesting at the FD relay outperforms that of the single-antenna. Moreover, our results demonstrate that FD relay systems always substantially boost the energy efficiency compared with half-duplex (HD) relay systems.<\/jats:p>","DOI":"10.3390\/fi11100205","type":"journal-article","created":{"date-parts":[[2019,9,20]],"date-time":"2019-09-20T10:48:14Z","timestamp":1568976494000},"page":"205","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Time and Power Allocation for Energy Efficiency Maximization in Wireless-Powered Full-Duplex Relay Systems"],"prefix":"10.3390","volume":"11","author":[{"given":"Xin","family":"Song","sequence":"first","affiliation":[{"name":"Engineering Optimization and Smart Antenna Institute, Northeastern University, Qinhuangdao 066100, China"},{"name":"School of Computer Science and Engineering, Northeastern University, Shenyang 110004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1555-675X","authenticated-orcid":false,"given":"Yue","family":"Ni","sequence":"additional","affiliation":[{"name":"Engineering Optimization and Smart Antenna Institute, Northeastern University, Qinhuangdao 066100, China"},{"name":"School of Computer Science and Engineering, Northeastern University, Shenyang 110004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5443-4742","authenticated-orcid":false,"given":"Xiuwei","family":"Han","sequence":"additional","affiliation":[{"name":"Engineering Optimization and Smart Antenna Institute, Northeastern University, Qinhuangdao 066100, China"},{"name":"School of Computer Science and Engineering, Northeastern University, Shenyang 110004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"Qin","sequence":"additional","affiliation":[{"name":"Engineering Optimization and Smart Antenna Institute, Northeastern University, Qinhuangdao 066100, China"},{"name":"School of Computer Science and Engineering, Northeastern University, Shenyang 110004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Dong","sequence":"additional","affiliation":[{"name":"Engineering Optimization and Smart Antenna Institute, Northeastern University, Qinhuangdao 066100, China"},{"name":"School of Computer Science and Engineering, Northeastern University, Shenyang 110004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3543","DOI":"10.1109\/TWC.2010.091510.100447","article-title":"Voluntary Energy Harvesting Relays and Selection in Cooperative Wireless Networks","volume":"9","author":"Medepally","year":"2010","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1109\/MC.2012.250","article-title":"Bond Graph Modeling for Energy-Harvesting Wireless Sensor Networks","volume":"45","author":"Venkata","year":"2012","journal-title":"Computer"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Varshney, L. (2008, January 6\u201311). Transporting information and energy simultaneously. Proceedings of the 2008 IEEE International Symposium on Information Theory, Toronto, ON, Canada.","DOI":"10.1109\/ISIT.2008.4595260"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Grover, P., and Sahai, A. (2010, January 13\u201318). Shannon meets Tesla: Wireless information and power transfer. Proceedings of the 2010 IEEE International Symposium on Information Theory, Austin, TX, USA.","DOI":"10.1109\/ISIT.2010.5513714"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1607","DOI":"10.1109\/TCOMM.2015.2415480","article-title":"Wireless-powered relays in cooperative communications: Time-switching relaying protocols and throughput analysis","volume":"63","author":"Nasir","year":"2015","journal-title":"IEEE Trans. Commun."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1109\/LCOMM.2015.2498151","article-title":"Joint Power Control and Time Switching for SWIPT Systems with Heterogeneous QoS Requirements","volume":"20","author":"Dong","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1186\/s13638-015-0288-3","article-title":"Cooperative wireless energy harvesting and information transfer in stochastic networks","volume":"2015","author":"Zhai","year":"2015","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"key":"ref_8","unstructured":"Liu, L., Zhang, R., and Chua, K.C. (2013, January 16\u201318). Wireless information and power transfer in an underlay cognitive radio network. Proceedings of the International Conference on Signal Processing and Communication Systems (ICSPCS), Gold Coast, Australia."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3390","DOI":"10.1109\/TCOMM.2013.071813.130105","article-title":"Wireless Information and Power Transfer: A Dynamic Power Splitting Approach","volume":"61","author":"Liu","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhong, C.J., Himal, A.S., and Zheng, G. (2015, January 8\u201312). Improving the Throughput of Wireless Powered Dual-hop Systems with Full Duplex Relaying. Proceedings of the 2015 IEEE International Conference on Communications (ICC), London, UK.","DOI":"10.1109\/ICC.2015.7248991"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"784","DOI":"10.1109\/LCOMM.2016.2535114","article-title":"Wireless Information and Power Transfer for Multirelay-Assisted Cooperative Communication","volume":"20","author":"Liu","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_12","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_13","doi-asserted-by":"crossref","first-page":"2573","DOI":"10.1109\/ACCESS.2017.2672868","article-title":"Wireless Power Transfer Strategies for Cooperative Relay System to Maximize Information Throughput","volume":"5","author":"Zhang","year":"2017","journal-title":"IEEE Access"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3828","DOI":"10.1109\/TVT.2015.2443875","article-title":"Outage Performance of Cognitive Relay Networks with Wireless Information and Power Transfer","volume":"65","author":"Yang","year":"2016","journal-title":"IEEE Trans. Veh. Tech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"6352","DOI":"10.1109\/TWC.2013.103113.130470","article-title":"Wireless Information and Power Transfer: Energy Efficiency Optimization in OFDMA Systems","volume":"12","author":"Ng","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1109\/ACCESS.2016.2549641","article-title":"Power Optimization in 5G Networks: A Step Towards Green Communication","volume":"4","author":"Abrol","year":"2016","journal-title":"IEEE Access"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"6425","DOI":"10.1109\/TWC.2015.2453418","article-title":"RF-Based Energy Harvesting in Decode-and Forward Relay Systems: Ergodic and Outage Capacities","volume":"14","author":"Gu","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5983","DOI":"10.1109\/TSP.2011.2164910","article-title":"Mitigation of Loopback Self-Interference in Full-Duplex MIMO Relays","volume":"59","author":"Riihonen","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","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_20","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.1109\/JSAC.2012.120921","article-title":"Full-Duplex MIMO Relaying: Achievable Rates Under Limited Dynamic Range","volume":"30","author":"Day","year":"2012","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1637","DOI":"10.1109\/JSAC.2014.2330193","article-title":"In-Band Full-Duplex Wireless: Challenges and Opportunities","volume":"32","author":"Sabharwal","year":"2014","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4381","DOI":"10.1109\/TWC.2012.101912.111944","article-title":"Full-Duplex Relay Selection for Amplify-and-Forward Cooperative Networks","volume":"11","author":"Krikidis","year":"2012","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_23","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_24","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":"Zhang","year":"2014","journal-title":"IEEE Trans. Commun."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Lee, C.-H., Chang, R.Y., Lin, C.-T., and Cheng, S.-M. (2017, January 8\u201313). Sum-rate maximization for energy harvesting-aided D2D communications underlaid cellular networks. Proceedings of the 2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), Montreal, QC, Canada.","DOI":"10.1109\/PIMRC.2017.8292471"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"6348","DOI":"10.1109\/TWC.2017.2723564","article-title":"Transmission Rate Optimization of Full-Duplex Relay Systems Powered by Wireless Energy Transfer","volume":"16","author":"Zhao","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_27","first-page":"4754","article-title":"Wireless information and power transfer: Architecture design and rate-energy tradeoff","volume":"61","author":"Zhou","year":"2013","journal-title":"IEEE Commun. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Mou, W., Cai, Y., Yang, W., Yang, W., Xu, X., and Hu, J. (2015, January 15\u201317). Exploiting full Duplex techniques for secure communication in SWIPT system. Proceedings of the International Conference on Wireless Communications & Signal Processing (WCSP), Nanjing, China.","DOI":"10.1109\/WCSP.2015.7341300"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1700","DOI":"10.1109\/TSP.2015.2396009","article-title":"Harvest-Then-Cooperate: Wireless-Powered Cooperative Communications","volume":"63","author":"Chen","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_30","first-page":"3622","article-title":"Relaying protocols for wireless energy harvesting and information processing","volume":"12","author":"Nasir","year":"2013","journal-title":"IEEE Commun. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Bharadia, D., McMilin, E., and Katti, S. (2013, January 12\u201316). Full duplex radios. Proceedings of the 2013 ACM SIGCOMM, Hong Kong, China.","DOI":"10.1145\/2486001.2486033"},{"key":"ref_32","first-page":"574","article-title":"Physical layer network security in the full-duplex relay system","volume":"10","author":"Chen","year":"2015","journal-title":"IEEE Access"}],"container-title":["Future Internet"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-5903\/11\/10\/205\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:22:16Z","timestamp":1760188936000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-5903\/11\/10\/205"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,20]]},"references-count":32,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2019,10]]}},"alternative-id":["fi11100205"],"URL":"https:\/\/doi.org\/10.3390\/fi11100205","relation":{},"ISSN":["1999-5903"],"issn-type":[{"type":"electronic","value":"1999-5903"}],"subject":[],"published":{"date-parts":[[2019,9,20]]}}}