{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:13:59Z","timestamp":1760242439776,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2017,8,23]],"date-time":"2017-08-23T00:00:00Z","timestamp":1503446400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61671347","61401330"],"award-info":[{"award-number":["61671347","61401330"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Natural Science Foundation of Shaanxi Province","award":["2016JQ6027"],"award-info":[{"award-number":["2016JQ6027"]}]},{"name":"the 111 project of China","award":["B08038"],"award-info":[{"award-number":["B08038"]}]},{"name":"the Natural Science Fundation of China","award":["61771368"],"award-info":[{"award-number":["61771368"]}]},{"name":"the key technology R&amp;D program of Henan province","award":["142102210572"],"award-info":[{"award-number":["142102210572"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Energy harvesting, which offers a never-ending energy supply, has emerged as a prominent technology to prolong the lifetime and reduce costs for the battery-powered wireless sensor networks. However, how to improve the energy efficiency while guaranteeing the quality of service (QoS) for energy harvesting based wireless sensor networks is still an open problem. In this paper, we develop statistical delay-bounded QoS-driven power control policies to maximize the effective energy efficiency (EEE), which is defined as the spectrum efficiency under given specified QoS constraints per unit harvested energy, for energy harvesting based wireless sensor networks. For the battery-infinite wireless sensor networks, our developed QoS-driven power control policy converges to the Energy harvesting Water Filling (E-WF) scheme and the Energy harvesting Channel Inversion (E-CI) scheme under the very loose and stringent QoS constraints, respectively. For the battery-finite wireless sensor networks, our developed QoS-driven power control policy becomes the Truncated energy harvesting Water Filling (T-WF) scheme and the Truncated energy harvesting Channel Inversion (T-CI) scheme under the very loose and stringent QoS constraints, respectively. Furthermore, we evaluate the outage probabilities to theoretically analyze the performance of our developed QoS-driven power control policies. The obtained numerical results validate our analysis and show that our developed optimal power control policies can optimize the EEE over energy harvesting based wireless sensor networks.<\/jats:p>","DOI":"10.3390\/s17091933","type":"journal-article","created":{"date-parts":[[2017,8,23]],"date-time":"2017-08-23T11:32:27Z","timestamp":1503487947000},"page":"1933","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Statistical-QoS Guaranteed Energy Efficiency Optimization for Energy Harvesting Wireless Sensor Networks"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3505-516X","authenticated-orcid":false,"given":"Ya","family":"Gao","sequence":"first","affiliation":[{"name":"State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019an 710071, China"},{"name":"College of Physics and Electronic Information&Henan Key Laboratory of Electromagnetic Transformation and Detection, Luoyang Normal University, Luoyang 471934, China"}]},{"given":"Wenchi","family":"Cheng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019an 710071, China"}]},{"given":"Hailin","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019an 710071, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,8,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gao, Y., Cheng, W., Zhang, W., and Zhang, H. (2017, January 4\u20138). Energy Efficiency Optimization With Statistical QoS Provisioning for Energy Harvesting Networks. Proceedings of the IEEE Global Conference on Communications, Singapore. accepted.","DOI":"10.1109\/GLOCOM.2017.8254041"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1109\/SURV.2011.060710.00094","article-title":"Energy Harvesting Sensor Nodes: Survey and Implications","volume":"13","author":"Sudevalayam","year":"2011","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4808","DOI":"10.1109\/TSP.2012.2199984","article-title":"Optimal energy allocation for wireless communications with energy harvesting constraints","volume":"60","author":"Ho","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1732","DOI":"10.1109\/JSAC.2011.110921","article-title":"Transmission with energy harvesting nodes in fading wireless channels: Optimal policies","volume":"29","author":"Ozel","year":"2011","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6869","DOI":"10.3390\/s90906869","article-title":"An Overview on Wireless Sensor Networks Technology and Evolution","volume":"9","author":"Buratti","year":"2009","journal-title":"Sensors"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1109\/MWC.2015.7054723","article-title":"Opportunistic communications in interference alignment networks with wireless power transfer","volume":"22","author":"Zhao","year":"2015","journal-title":"IEEE Wirel. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4405","DOI":"10.1109\/TCOMM.2015.2478782","article-title":"Energy-Efficient Cooperative Transmission for Simultaneous Wireless Information and Power Transfer in Clustered Wireless Sensor Networks","volume":"63","author":"Guo","year":"2015","journal-title":"IEEE Trans. Commun."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1109\/COMST.2014.2368999","article-title":"Wireless networks with RF energy harvesting: A contemporary survey","volume":"17","author":"Lu","year":"2015","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_9","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_10","doi-asserted-by":"crossref","first-page":"3709","DOI":"10.1109\/JSAC.2016.2611846","article-title":"Green full-duplex self-backhaul and energy harvesting small cell networks with massive MIMO","volume":"34","author":"Chen","year":"2016","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"6434","DOI":"10.1109\/TWC.2016.2585115","article-title":"Energy allocation and cooperation for energy-efficient wireless two-tier networks","volume":"15","author":"Ramamonjison","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4268","DOI":"10.1109\/TVT.2014.2362005","article-title":"Adaptive energy-efficient power allocation in green interference-alignment-based wireless networks","volume":"64","author":"Zhao","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3438","DOI":"10.1109\/JSAC.2016.2611843","article-title":"Energy efficiency resource allocation for wireless power transfer enabled collaborative mobile clouds","volume":"34","author":"Chang","year":"2016","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"9834","DOI":"10.1109\/TVT.2016.2525821","article-title":"Energy efficiency resource allocation and user scheduling for collaborative mobile clouds with hybrid receivers","volume":"65","author":"Chang","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"6132","DOI":"10.1109\/TWC.2016.2578925","article-title":"Optimum transmission policies for energy harvesting sensor networks powered by a mobile control center","volume":"15","author":"Li","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_16","first-page":"1505","article-title":"Data-driven stochastic models and policies for energy harvesting sensor communications","volume":"33","author":"Ku","year":"2015","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1327","DOI":"10.1109\/TMTT.2016.2533619","article-title":"Sensitive and efficient RF harvesting supply for batteryless backscatter sensor networks","volume":"64","author":"Assimonis","year":"2016","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4776","DOI":"10.1109\/TCOMM.2016.2602863","article-title":"QoS-Aware Throughput Maximization in Wireless Powered Underground Sensor Networks","volume":"64","author":"Liu","year":"2016","journal-title":"IEEE Trans. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Niyato, D., Lu, X., Wang, P., Kim, D., and Han, Z. (2016, January 22\u201327). Distributed Wireless Energy Scheduling for Wireless Powered Sensor Networks. Proceedings of the IEEE International Conference on Communications (ICC 2016), Kuala Lumper, Malaysia.","DOI":"10.1109\/ICC.2016.7510699"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1109\/JSAC.2010.100413","article-title":"Statistical QoS provisionings for wireless unicast\/multicast of multi-layer video streams","volume":"28","author":"Du","year":"2010","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_21","first-page":"630","article-title":"Effective capacity: A wireless link model for support of quality of service","volume":"2","author":"Wu","year":"2003","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1109\/JSAC.2013.130509","article-title":"Joint spectrum and power efficiencies optimization for statistical QoS provisionings over SISO\/MIMO wireless networks","volume":"31","author":"Cheng","year":"2013","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"6896","DOI":"10.1109\/TWC.2015.2462816","article-title":"Optimal power allocation for underlay-based cognitive radio networks with primary user\u2019s statistical delay QoS provisioning","volume":"14","author":"Wang","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1109\/MCOM.2015.7081082","article-title":"Provisioning quality-of-service to energy harvesting wireless communications","volume":"53","author":"Chen","year":"2015","journal-title":"IEEE Commun. Mag."},{"key":"ref_25","first-page":"5113","article-title":"QoS provisioning based resource allocation for energy harvesting systems","volume":"15","author":"Loodaricheh","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Ibarra, E., Antonopoulos, A., Kartsakli, E., Rodrigues, J., and Verikoukis, C. (2014, January 10\u201314). Joint Power-QoS Control Scheme for Energy Harvesting Body Sensor Nodes. Proceedings of the IEEE International Conference on Communications (ICC 2014), Sydney, Australia.","DOI":"10.1109\/ICC.2014.6883865"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Gong, J., Zhang, S., Wang, X., Zhou, S., and Niu, Z. (2014, January 10\u201314). Supporting quality of service in energy harvesting wireless links: The effective capacity analysis. Proceedings of the 2014 IEEE International Conference on Communications Workshops (ICC), Sydney, Australia.","DOI":"10.1109\/ICCW.2014.6881315"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Zhang, H., Du, Q., Ren, P., and Sun, L. (2015, January 6\u201310). Joint battery-buffer sustainable guarantees in energy-harvesting enabled wireless networks. Proceedings of the IEEE Global Communications Conference (GLOBECOM 2015), Sandiego, CA, USA.","DOI":"10.1109\/GLOCOM.2015.7417511"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1109\/9.284868","article-title":"Stability, Queue Length, and Delay of Deterministic and Stochastic Queueing Networks","volume":"39","author":"Chang","year":"1994","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"7910","DOI":"10.1109\/ACCESS.2017.2694046","article-title":"Heterogeneous Statistical QoS Provisioning Over Wireless Powered Sensor Networks","volume":"5","author":"Gao","year":"2017","journal-title":"IEEE Access"},{"key":"ref_31","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_32","doi-asserted-by":"crossref","first-page":"1116","DOI":"10.1109\/JSAC.2016.2520244","article-title":"Energy-aware traffic offloading for green heterogeneous networks","volume":"34","author":"Zhang","year":"2016","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_33","unstructured":"Erhan, C. (1975). Introduction to Stocastic Processes, Prentice-Hall."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Boyd, S., and Vandenberghe, L. (2004). Convex Optimization, Cambridge University Press.","DOI":"10.1017\/CBO9780511804441"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1196","DOI":"10.1109\/TWC.2013.012413.120488","article-title":"Optimal save-then-transmit protocol for energy harvesting wireless transmitters","volume":"12","author":"Luo","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"972","DOI":"10.1109\/TVT.2015.2402274","article-title":"Outage probability of energy harvesting relay-aided cooperative networks over rayleigh fading channel","volume":"65","author":"Li","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_37","unstructured":"Klenke, A. (2008). Probability Theory: A Comprehensive Course, Springer."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1109\/TW.2013.121813.130953","article-title":"Optimal power allocation for outage probability minimization in fading channels with energy harvesting constraints","volume":"13","author":"Huang","year":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1109\/JSAC.2015.2391951","article-title":"Outage minimization for a fading wireless link with energy harvesting transmitter and receiver","volume":"33","author":"Zhou","year":"2015","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Tse, D., and Viswanath, P. (2005). Fundamentals of Wireless Communication, Cambridge University Press.","DOI":"10.1017\/CBO9780511807213"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/9\/1933\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:43:04Z","timestamp":1760208184000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/9\/1933"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,23]]},"references-count":40,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2017,9]]}},"alternative-id":["s17091933"],"URL":"https:\/\/doi.org\/10.3390\/s17091933","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,8,23]]}}}