{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:10:20Z","timestamp":1760191820560,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2019,11,4]],"date-time":"2019-11-04T00:00:00Z","timestamp":1572825600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61771206","61801184"],"award-info":[{"award-number":["61771206","61801184"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Device-to-device (D2D) communication, as one of the promising candidates for the fifth generation mobile network, can afford effective service of new mobile applications and business models. In this paper, we study the resource management strategies for D2D communication underlying the cellular networks. To cater for green communications, our design goal is to the maximize ergodic energy efficiency (EE) of all D2D links taking into account the fact that it may be tricky for the base station (BS) to receive all the real-time channel state information (CSI) while guaranteeing the stability and the power requirements for D2D links. We formulate the optimization problem which is difficult to resolve directly because of its non-convex nature. Then a novel maximum weighted ergodic energy efficiency (MWEEE) algorithm is proposed to solve the formulated optimization problem which consists of two sub-problems: the power control (PC) sub-problem which can be solved by employing convex optimization theory for both cellular user equipment (CUE) and D2D user equipment (DUE) and the channel allocation (CA) sub-problem which can be solved by obtaining the weighted allocation matrix. In particular, we shed light into the impact on EE metric of D2D communication by revealing the nonlinear power relationship between CUE and DUE and taking the QoS of CUEs into account. Furthermore, simulation results show that our proposed algorithm is superior to the existing algorithms.<\/jats:p>","DOI":"10.3390\/s19214799","type":"journal-article","created":{"date-parts":[[2019,11,4]],"date-time":"2019-11-04T10:49:07Z","timestamp":1572864547000},"page":"4799","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Joint Power and Channel Scheduling Scheme for Underlay D2D Communications in the Cellular Network"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0877-2326","authenticated-orcid":false,"given":"Zefang","family":"Lin","sequence":"first","affiliation":[{"name":"School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510631, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0458-5136","authenticated-orcid":false,"given":"Hui","family":"Song","sequence":"additional","affiliation":[{"name":"School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510631, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6919-7209","authenticated-orcid":false,"given":"Daru","family":"Pan","sequence":"additional","affiliation":[{"name":"School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510631, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"15184","DOI":"10.1109\/ACCESS.2017.2678508","article-title":"Energy-efficient stable matching for resource allocation in energy harvesting-based device-to-device communications","volume":"5","author":"Zhou","year":"2017","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"10486","DOI":"10.1109\/TVT.2017.2727144","article-title":"Resource allocation for energy harvesting-powered D2D communication underlaying cellular networks","volume":"66","author":"Luo","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3217","DOI":"10.1109\/TCOMM.2018.2812731","article-title":"Power control and channel allocation for D2D underlaid cellular networks","volume":"66","author":"Abdallah","year":"2018","journal-title":"IEEE Trans. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"32409","DOI":"10.1109\/ACCESS.2018.2839190","article-title":"System capacity maximization with efficient resource allocation algorithms in D2D communication","volume":"6","author":"Hussain","year":"2018","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Yu, B., Zhang, X., Palmieri, F., Creignou, E., and You, I. (2019). A Deep Learning Approach for Maximum Activity Links in D2D Communications. Sensors, 19.","DOI":"10.3390\/s19132941"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Nitti, M., Stelea, G.A., Popescu, V., and Fadda, M. (2019). When social networks meet D2D communications: A survey. Sensors, 19.","DOI":"10.3390\/s19020396"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3534","DOI":"10.1109\/TCOMM.2016.2580153","article-title":"Mode selection, resource allocation, and power control for D2D-enabled two-tier cellular network","volume":"64","author":"Huang","year":"2016","journal-title":"IEEE Trans. Commun."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1109\/LCOMM.2016.2617863","article-title":"Joint mode selection and resource allocation for relay-based D2D communications","volume":"21","author":"Hoang","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"9787","DOI":"10.1109\/TVT.2016.2531290","article-title":"QoS-oriented mode, spectrum, and power allocation for D2D communication underlaying LTE-A network","volume":"65","author":"Asheralieva","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1466","DOI":"10.1109\/TWC.2016.2646360","article-title":"Distributed power allocation for D2D communications underlaying\/overlaying OFDMA cellular networks","volume":"16","author":"Abrardo","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1109\/LCOMM.2017.2771778","article-title":"Distributed resource allocation for D2D communications underlaying cellular networks in time-varying environment","volume":"22","author":"Dominic","year":"2017","journal-title":"IEEE Commun. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1109\/TVT.2018.2878195","article-title":"Incentive design for cache-enabled D2D underlaid cellular networks using Stackelberg Game","volume":"68","author":"Shi","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2156","DOI":"10.1109\/JSAC.2015.2435361","article-title":"Matching and cheating in device to device communications underlying cellular networks","volume":"33","author":"Gu","year":"2015","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1088","DOI":"10.3390\/s17051088","article-title":"An interference mitigation scheme of device-to-device communications for sensor networks underlying LTE-A","volume":"17","author":"Kim","year":"2017","journal-title":"Sensors"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1159","DOI":"10.1109\/TVT.2016.2553124","article-title":"Resource allocation for D2D communications underlay in Rayleigh fading channels","volume":"66","author":"Wang","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_16","first-page":"467","article-title":"Power allocation for underlay device-to-device communication over multiple channels","volume":"4","author":"AliHemmati","year":"2017","journal-title":"IEEE Trans. Signal Inf. Process. Netw."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"7594","DOI":"10.1109\/TWC.2016.2604813","article-title":"Optimal QoS-aware channel assignment in D2D communications with partial CSI","volume":"15","author":"Wang","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"6244","DOI":"10.1109\/TVT.2018.2817613","article-title":"Resource allocation for underlay D2D communication with proportional fairness","volume":"67","author":"Li","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4118","DOI":"10.1109\/TWC.2018.2820693","article-title":"Socially aware secrecy-ensured resource allocation in D2D underlay communication: An overlapping coalitional game scheme","volume":"17","author":"Ahmed","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3541","DOI":"10.1109\/TCOMM.2013.071013.120787","article-title":"Device-to-device communications underlaying cellular networks","volume":"61","author":"Feng","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3186","DOI":"10.1109\/TCOMM.2017.2699194","article-title":"Resource allocation for D2D-enabled vehicular communications","volume":"65","author":"Liang","year":"2017","journal-title":"IEEE Trans. Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1109\/LWC.2014.2337295","article-title":"Energy efficiency and spectral efficiency tradeoff in device-to-device (D2D) communications","volume":"3","author":"Zhou","year":"2014","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"4288","DOI":"10.1109\/TWC.2018.2822284","article-title":"Energy-spectral efficiency trade-off in underlaying mobile D2D communications: An economic efficiency perspective","volume":"17","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_24","first-page":"2097","article-title":"Energy-efficient resource reuse scheme for D2D communications underlaying cellular networks","volume":"21","author":"Hu","year":"2017","journal-title":"IEEE Commun. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4936","DOI":"10.1109\/TCOMM.2018.2834920","article-title":"Robust multi-objective optimization for EE-SE tradeoff in D2D communications underlaying heterogeneous networks","volume":"66","author":"Hao","year":"2018","journal-title":"IEEE Trans. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1542","DOI":"10.1109\/TII.2017.2789304","article-title":"Energy-efficient device-to-device communications for green smart cities","volume":"14","author":"Kai","year":"2018","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"31385","DOI":"10.1109\/ACCESS.2019.2903214","article-title":"Towards Energy-Efficient Underlaid Device-to-Device Communications: A Joint Resource Management Approach","volume":"7","author":"Zhang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Hmila, M., Fern\u00e1ndez-Veiga, M., Rodr\u00edguez-P\u00e9rez, M., and Herrer\u00eda-Alonso, S. (2019). Energy Efficient Power and Channel Allocation in Underlay Device to Multi Device Communications. IEEE Trans. Commun.","DOI":"10.1109\/TCOMM.2019.2915227"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1109\/JIOT.2018.2842738","article-title":"Energy efficient resource allocation algorithm in energy harvesting-based D2D heterogeneous networks","volume":"6","author":"Kuang","year":"2018","journal-title":"IEEE Internet Things J."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1109\/TVT.2018.2881545","article-title":"Energy-efficient resource allocation for energy harvesting-based device-to-device communication","volume":"68","author":"Dai","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3628","DOI":"10.1109\/TVT.2015.2450774","article-title":"Social-community-aware resource allocation for D2D communications underlaying cellular networks","volume":"65","author":"Wang","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1109\/TWC.2016.2625255","article-title":"Interference-constrained pricing for D2D networks","volume":"16","author":"Liu","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4163","DOI":"10.1109\/TWC.2018.2821151","article-title":"Resource allocation for device-to-device communications underlaying heterogeneous cellular networks using coalitional games","volume":"17","author":"Chen","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1287\/mnsc.13.7.492","article-title":"On nonlinear fractional programming","volume":"13","author":"Dinkelbach","year":"1967","journal-title":"Manag. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1540","DOI":"10.1109\/LSP.2018.2864620","article-title":"Solving Fractional Polynomial Problems by Polynomial Optimization Theory","volume":"25","author":"Pizzo","year":"2018","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"4157","DOI":"10.1109\/TWC.2019.2922609","article-title":"Reconfigurable intelligent surfaces for energy efficiency in wireless communication","volume":"18","author":"Huang","year":"2019","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3711","DOI":"10.1109\/TIT.2009.2023751","article-title":"SCALE: A low-complexity distributed protocol for spectrum balancing in multiuser DSL networks","volume":"55","author":"Papandriopoulos","year":"2009","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Boyd, S., and Vandenberghe, L. (2004). Convex Optimization, Cambridge University Press.","DOI":"10.1017\/CBO9780511804441"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"354","DOI":"10.2307\/3619777","article-title":"A new approach to solving the cubic: Cardan\u2019s solution revealed","volume":"77","author":"Nickalls","year":"1993","journal-title":"Math. Gaz."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/21\/4799\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:31:50Z","timestamp":1760189510000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/21\/4799"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,4]]},"references-count":39,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2019,11]]}},"alternative-id":["s19214799"],"URL":"https:\/\/doi.org\/10.3390\/s19214799","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,11,4]]}}}