{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T14:56:20Z","timestamp":1775487380665,"version":"3.50.1"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,4,13]],"date-time":"2024-04-13T00:00:00Z","timestamp":1712966400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,4,13]],"date-time":"2024-04-13T00:00:00Z","timestamp":1712966400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Wireless Com Network"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, we improve networks\u2019 spectral efficiency (SE), extend networks\u2019 lifetime, and maximize networks\u2019 energy efficiency (EE) of two-way full-duplex (FD) relay networks. Firstly, to improve networks\u2019 SE and to extend networks\u2019 lifetime simultaneously, we design a two-way FD relay transmission strategy with simultaneous wireless information and power transfer and direct links (DLs). The designed transmission strategy can complete a bidirectional communication in only one time slot with the exists of DLs and the energy-constrained relay node. With the designed transmission strategy, we further give the characteristics of relay amplification factor, the analysis of the designed transmission strategy, and the EE analysis of traditional half-duplex two-way amplify-and-forward relaying. Secondly, to maximize networks\u2019 EE, we present both the EE maximization problems and analyses of the designed transmission strategy with equal power allocation and optimal power allocation. To solve the EE maximization problems, we further propose the alternating optimal algorithm and give complexity analysis of the algorithm. Simulations show that our designed transmission strategy can improve the SE and EE of the networks.<\/jats:p>","DOI":"10.1186\/s13638-024-02344-w","type":"journal-article","created":{"date-parts":[[2024,4,13]],"date-time":"2024-04-13T11:01:58Z","timestamp":1713006118000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Energy-efficient two-way full-duplex relay transmission strategy with SWIPT and direct links"],"prefix":"10.1186","volume":"2024","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5536-7617","authenticated-orcid":false,"given":"Caixia","family":"Cai","sequence":"first","affiliation":[]},{"given":"Fuli","family":"Zhong","sequence":"additional","affiliation":[]},{"given":"Han","family":"Hai","sequence":"additional","affiliation":[]},{"given":"Mingzhi","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Wenyang","family":"Gan","sequence":"additional","affiliation":[]},{"given":"Bing","family":"Sun","sequence":"additional","affiliation":[]},{"given":"Yayu","family":"Yang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,13]]},"reference":[{"issue":"7","key":"2344_CR1","first-page":"1000","volume":"9","author":"H Azarhsvs","year":"2020","unstructured":"H. Azarhsvs, J.M. Niya, Energy efficient resource allocation in wireless energy harvesting sensor networks. IEEE Wirel. Commun. Lett. 9(7), 1000\u20131003 (2020)","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"2344_CR2","doi-asserted-by":"crossref","unstructured":"Y. Zheng , J. Hu, K. Yang, SWIPT aided cooperative communications with energy harvesting based selective-decode-and-forward protocol: benefiting from channel aging effect. IEEE Trans. Green Commun. Netw. (2023) (early access)","DOI":"10.1109\/TGCN.2023.3281606"},{"issue":"2","key":"2344_CR3","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1109\/LCOMM.2018.2883432","volume":"23","author":"D-W Lim","year":"2019","unstructured":"D.-W. Lim, J. Kang, C.-J. Chun, H.-M. Kim, Joint transmit power and time-switching control for device-to-device communications in SWIPT cellular networks. IEEE Commun. Lett. 23(2), 322\u2013325 (2019)","journal-title":"IEEE Commun. Lett."},{"issue":"11","key":"2344_CR4","doi-asserted-by":"publisher","first-page":"10813","DOI":"10.1109\/JIOT.2020.2988512","volume":"7","author":"H Yang","year":"2020","unstructured":"H. Yang, Y. Ye, X. Chu, M. Dong, Resource and power allocation in SWIPT enabled device-to-device communications based on a non-linear energy harvesting model. IEEE Internet Things J. 7(11), 10813\u201310825 (2020)","journal-title":"IEEE Internet Things J."},{"key":"2344_CR5","doi-asserted-by":"crossref","unstructured":"X.\u00a0Ji, T.\u00a0Wang, Energy minimization for fixed-wing UAV assisted full-duplex relaying with bank angle constraint. IEEE Wirel. Commun. Lett. 1\u20131 (2023) (early access)","DOI":"10.1109\/LWC.2023.3266434"},{"issue":"5","key":"2344_CR6","doi-asserted-by":"publisher","first-page":"1640","DOI":"10.1109\/LCOMM.2021.3057387","volume":"25","author":"L Li","year":"2021","unstructured":"L. Li, T. Wu, J. Qin, Sum achievable rate maximization in orbital angular momentum-based amplify-and-forward two-way relay networks. IEEE Wirel. Commun. Lett. 25(5), 1640\u20131644 (2021)","journal-title":"IEEE Wirel. Commun. Lett."},{"issue":"5","key":"2344_CR7","doi-asserted-by":"publisher","first-page":"3532","DOI":"10.1109\/TSP.2012.2191543","volume":"61","author":"H Wang","year":"2012","unstructured":"H. Wang, Q. Yin, X.-G. Xia, Distributed beamforming for physical-layer security of two-way relay networks. IEEE Trans. Signal Process. 61(5), 3532\u20133545 (2012)","journal-title":"IEEE Trans. Signal Process."},{"issue":"10","key":"2344_CR8","doi-asserted-by":"publisher","first-page":"4893","DOI":"10.1109\/TVT.2014.2370754","volume":"64","author":"H Wang","year":"2015","unstructured":"H. Wang, F. Liu, M. Yang, Joint cooperative beamforming, jamming and power allocation to secure AF relay systems. IEEE Trans. Veh. Technol. 64(10), 4893\u20134898 (2015)","journal-title":"IEEE Trans. Veh. Technol."},{"issue":"2","key":"2344_CR9","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1109\/TGCN.2019.2906616","volume":"3","author":"A Gupta","year":"2019","unstructured":"A. Gupta, K. Singh, M. Sellathurai, Time-switching EH based joint relay selection and resource allocation algorithms for multi-user multicarrier AF relay networks. IEEE Trans. Green Commun. Netw. 3(2), 505\u2013522 (2019)","journal-title":"IEEE Trans. Green Commun. Netw."},{"issue":"2","key":"2344_CR10","doi-asserted-by":"publisher","first-page":"1199","DOI":"10.1109\/TWC.2017.2776933","volume":"17","author":"Y Feng","year":"2018","unstructured":"Y. Feng, V.C.M. Leung, F. Ji, Performance study for SWIPT cooperative communication systems in shadowed Nakagami fading channels. IEEE Trans. Wirel. Commun. 17(2), 1199\u20131211 (2018)","journal-title":"IEEE Trans. Wirel. Commun."},{"issue":"4","key":"2344_CR11","doi-asserted-by":"publisher","first-page":"1072","DOI":"10.1109\/TGCN.2018.2856363","volume":"2","author":"L Mohjazi","year":"2018","unstructured":"L. Mohjazi, S. Muhaidat, M. Dianati, M. Al-Qutayri, Performance analysis of SWIPT relay networks with noncoherent modulation. IEEE Trans. Green Commun. Netw. 2(4), 1072\u20131086 (2018)","journal-title":"IEEE Trans. Green Commun. Netw."},{"issue":"9","key":"2344_CR12","doi-asserted-by":"publisher","first-page":"6264","DOI":"10.1109\/TWC.2017.2721372","volume":"16","author":"Q Cui","year":"2017","unstructured":"Q. Cui, Y. Zhang, W. Ni, M. Valkama, R. Janti, Energy efficiency maximization of full-duplex two-way relay with non-ideal power amplifiers and non-negligible circuit power. IEEE Trans. Wirel. Commun. 16(9), 6264\u20136278 (2017)","journal-title":"IEEE Trans. Wirel. Commun."},{"issue":"6","key":"2344_CR13","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1049\/el.2017.0032","volume":"53","author":"X Zhou","year":"2016","unstructured":"X. Zhou, Q. Li, Energy efficiency optimisation for SWIPT AF two-way relay networks. Electron. Lett. 53(6), 436\u2013438 (2016)","journal-title":"Electron. Lett."},{"issue":"7","key":"2344_CR14","doi-asserted-by":"publisher","first-page":"1014","DOI":"10.1109\/LSP.2018.2839036","volume":"25","author":"Y Ye","year":"2018","unstructured":"Y. Ye, Y. Li, Z. Wang, X. Chu, H. Zhang, Dynamic asymmetric power splitting scheme for SWIPT-based two-way multiplicative AF relaying. IEEE Signal Process. Lett. 25(7), 1014\u20131018 (2018)","journal-title":"IEEE Signal Process. Lett."},{"issue":"4","key":"2344_CR15","doi-asserted-by":"publisher","first-page":"982","DOI":"10.1109\/TGCN.2020.3008409","volume":"4","author":"MK Shukla","year":"2020","unstructured":"M.K. Shukla, H.H. Nguyen, O.J. Pandey, Multiuser full-duplex IoT networks with wireless-powered relaying: performance analysis and energy efficiency optimization. IEEE Trans. Green Commun. Netw. 4(4), 982\u2013997 (2020)","journal-title":"IEEE Trans. Green Commun. Netw."},{"issue":"12","key":"2344_CR16","doi-asserted-by":"publisher","first-page":"8473","DOI":"10.1109\/TWC.2018.2877752","volume":"17","author":"P Ju","year":"2018","unstructured":"P. Ju, M. Wen, X. Cheng, L. Yang, Achievable-rate-enhancing self-interference cancellation for full-duplex communications. IEEE Trans. Wirel. Commun. 17(12), 8473\u20138484 (2018)","journal-title":"IEEE Trans. Wirel. Commun."},{"issue":"58","key":"2344_CR17","doi-asserted-by":"publisher","first-page":"1572","DOI":"10.1109\/JSAC.2013.130819","volume":"31","author":"S Zhang","year":"2013","unstructured":"S. Zhang, S.C. Liew, H. Wang, Blind known interference cancellation. IEEE J. Sel. Areas Commun. 31(58), 1572\u20131582 (2013)","journal-title":"IEEE J. Sel. Areas Commun."},{"issue":"3","key":"2344_CR18","doi-asserted-by":"publisher","first-page":"3390","DOI":"10.1109\/JSYST.2019.2953949","volume":"14","author":"P Raut","year":"2020","unstructured":"P. Raut, T. Kaple, P.K. Sharma, Outage and average rate performances of full-duplex multiuser AF relay systems with time-selective fading. IEEE Syst. J. 14(3), 3390\u20133398 (2020)","journal-title":"IEEE Syst. J."},{"issue":"5","key":"2344_CR19","doi-asserted-by":"publisher","first-page":"3167","DOI":"10.1109\/TCOMM.2019.2899872","volume":"67","author":"M-K Chang","year":"2019","unstructured":"M.-K. Chang, F.-T. Chien, C.-H. Kuo, Y.-C. Chen, On the accumulated loopback self-interference of two-way full-duplex AF relaying systems. IEEE Trans. Commun. 67(5), 3167\u20133181 (2019)","journal-title":"IEEE Trans. Commun."},{"key":"2344_CR20","doi-asserted-by":"publisher","unstructured":"D. Wang, R. Zhang, X. Cheng, L. Yang, Relay selection in two-way full-duplex energy-harvesting relay networks, in Proceedings of 2016 IEEE Global Communications Conference (Globecom) (Washington, 2016), pp. 1\u20136. https:\/\/doi.org\/10.1109\/GLOCOM.2016.7842211","DOI":"10.1109\/GLOCOM.2016.7842211"},{"issue":"2","key":"2344_CR21","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1109\/TGCN.2017.2686325","volume":"1","author":"D Wang","year":"2017","unstructured":"D. Wang, R. Zhang, X. Cheng, L. Yang, C. Chen, Relay selection in full-duplex energy-harvesting two-way relay networks. IEEE Trans. Green Commun. Netw. 1(2), 182\u2013191 (2017)","journal-title":"IEEE Trans. Green Commun. Netw."},{"issue":"3","key":"2344_CR22","doi-asserted-by":"publisher","first-page":"2025","DOI":"10.1109\/TWC.2015.2497683","volume":"15","author":"Z He","year":"2016","unstructured":"Z. He, X. Zhang, Y. Bai, W. Jiang, Y. Rong, Optimal source and relay design for multiuser MIMO AF relay communication systems with direct links and imperfect channel information. IEEE Trans. Wirel. Commun. 15(3), 2025\u20132038 (2016)","journal-title":"IEEE Trans. Wirel. Commun."},{"issue":"3","key":"2344_CR23","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1109\/TGCN.2020.2979244","volume":"4","author":"C Cai","year":"2020","unstructured":"C. Cai, R. Qiu, X.Q. Jiang, Design and optimization for energy-efficient full-duplex transmission with direct links. IEEE Trans. Green Commun. Netw. 4(3), 689\u2013702 (2020)","journal-title":"IEEE Trans. Green Commun. Netw."},{"issue":"1","key":"2344_CR24","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1109\/TWC.2020.3023094","volume":"20","author":"Y Jiang","year":"2021","unstructured":"Y. Jiang, C. Wan, M. Tao, F.-C. Zheng, P. Zhu, X. Gao, X. You, Analysis and optimization of fog radio access networks with hybrid caching: delay and energy efficiency. IEEE Trans. Wirel. Commun. 20(1), 69\u201382 (2021)","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"2344_CR25","doi-asserted-by":"publisher","unstructured":"C.\u00a0Sun, C.\u00a0Yang, Energy efficiency comparison among direct, one-way and two-way relay transmission, in Proceedings of 2012 IEEE International Conference on Communications (ICC) (Ottawa, 2012), pp. 4288\u20134293. https:\/\/doi.org\/10.1109\/ICC.2012.6363882","DOI":"10.1109\/ICC.2012.6363882"},{"issue":"11","key":"2344_CR26","doi-asserted-by":"publisher","first-page":"24203","DOI":"10.1109\/ACCESS.2017.2771305","volume":"12","author":"J Yang","year":"2017","unstructured":"J. Yang, Z. He, Y. Rong, Transceiver optimization for two-hop MIMO relay systems with direct link and MSE constraints. IEEE Access 12(11), 24203\u201324213 (2017)","journal-title":"IEEE Access"},{"key":"2344_CR27","doi-asserted-by":"publisher","unstructured":"X. Cheng, B. Yu, X. Cheng, L. Yang, Two-way full-duplex amplify-and-forward relaying, in Proceedings of 2013 IEEE Military Communications Conference (Milcom) (San Diego, 2013), pp. 1\u20136. https:\/\/doi.org\/10.1109\/MILCOM.2013.9","DOI":"10.1109\/MILCOM.2013.9"},{"issue":"12","key":"2344_CR28","doi-asserted-by":"publisher","first-page":"10335","DOI":"10.1109\/TWC.2022.3183407","volume":"21","author":"Z Wang","year":"2023","unstructured":"Z. Wang, L. Liu, S. Zhang, P. Dong, Q. Yang, T. Wang, PNC enabled IIoT: a general framework for channel-coded asymmetric physical-layer network coding. IEEE Trans. Wirel. Commun. 21(12), 10335\u201310350 (2023)","journal-title":"IEEE Trans. Wirel. Commun."},{"issue":"2","key":"2344_CR29","doi-asserted-by":"publisher","first-page":"690","DOI":"10.1109\/TWC.2012.122212.120086","volume":"12","author":"J Xu","year":"2013","unstructured":"J. Xu, L. Qiu, Energy efficiency optimization for MIMO broadcast channels. IEEE Trans. Wirel. Commun. 12(2), 690\u2013701 (2013)","journal-title":"IEEE Trans. Wirel. Commun."},{"issue":"3\u20134","key":"2344_CR30","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1561\/0100000088","volume":"11","author":"A Zappone","year":"2015","unstructured":"A. Zappone, E. Jorswieck, Energy efficiency in wireless networks via fractional programming theory. Found. Trends Commun. Inf. Theory 11(3\u20134), 185\u2013396 (2015)","journal-title":"Found. Trends Commun. Inf. Theory"}],"container-title":["EURASIP Journal on Wireless Communications and Networking"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13638-024-02344-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s13638-024-02344-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13638-024-02344-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,13]],"date-time":"2024-04-13T11:04:49Z","timestamp":1713006289000},"score":1,"resource":{"primary":{"URL":"https:\/\/jwcn-eurasipjournals.springeropen.com\/articles\/10.1186\/s13638-024-02344-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,13]]},"references-count":30,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["2344"],"URL":"https:\/\/doi.org\/10.1186\/s13638-024-02344-w","relation":{},"ISSN":["1687-1499"],"issn-type":[{"value":"1687-1499","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,13]]},"assertion":[{"value":"21 July 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 April 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 April 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"17"}}