Energy-efficient cell-association bias adjustment algorithm for ultra-dense networks


In recent years, energy efficiency has become an important topic, especially in the field of ultra-dense networks (UDNs). In this area, cell-association bias adjustment and small cell on/off are proposed to enhance the performance of energy efficiency in UDNs. This is done by changing the cell association relationship and turning off the extra small cells that have no users. However, the variety of cell association relationships and the switching on/off of the small cells may deteriorate some users’ data rates, leading to nonconformance to the users’ data rate requirement. Considering the discreteness and non-convexity of the energy efficiency optimization problem and the coupled relationship between cell association and scheduling during the optimization process, it is difficult to achieve an optimal cell-association bias. In this study, we optimize the network energy efficiency by adjusting the cell-association bias of small cells while satisfying the users’ data rate requirement. We propose an energy-efficient centralized Gibbs sampling based cell-association bias adjustment (CGSCA) algorithm. In CGSCA, global information such as channel state information, cell association information, and network load information need to be collected. Then, considering the overhead of the messages that are exchanged and the implementation complexity of CGSCA to obtain the global information in UDNs, we propose an energy-efficient distributed Gibbs sampling based cell-association bias adjustment (DGSCA) algorithm with a lower message-exchange overhead and implementation complexity. Using DGSCA, we derive the updated formulas for calculating the number of users in a cell and the users’ SINR. We analyze the implementation complexities (e.g., computation complexity and communication com- plexity) of the proposed two algorithms and other existing algorithms. We perform simulations, and the results show that CGSCA and DGSCA have faster convergence speed, as well as a higher performance gain of the energy efficiency and throughput compared to other existing algorithms. In addition, we analyze the importance of the users’ data rate constraint in optimizing the energy efficiency, and we compare the energy efficiency performance of different algorithms with different number of small cells. Then, we present the number of sleeping small cells as the number of small cells increases.

This is a preview of subscription content, access via your institution.


  1. 1

    You X H, Pan Z W, Gao X Q, et al. The 5G mobile communication: the development trends and its emerging key techniques (in Chinese). Sci Sin Inform, 2014, 44: 551–563

    Google Scholar 

  2. 2

    Venturino L, Zappone A, Risi C, et al. E nergy-efficient scheduling and power allocation in downlink OFDMA networks with base station coordination. IEEE Trans Wirel Commun, 2015, 14: 1–14

    Article  Google Scholar 

  3. 3

    Osseiran A, Boccardi F, Braun V, et al. Scenarios for 5G mobile and wireless communications: the vision of the METIS project. IEEE Commun Mag, 2014, 52: 26–35

    Article  Google Scholar 

  4. 4

    Yang C G, Li J D, Guizani M. Cooperation for spectral and energy efficiency in ultra-dense small cell networks. IEEE Wirel Commun, 2016, 23: 64–71

    Article  Google Scholar 

  5. 5

    Cai S J, Che Y L, Duan L J, et al. Green 5G heterogeneous networks through dynamic small-cell operation. IEEE J Sel Areas Commun, 2016, 34: 1103–1115

    Article  Google Scholar 

  6. 6

    Ng D, Lo E, Schober R. Energy-efficient resource allocation in OFDMA systems with hybrid energy harvesting base station. IEEE Trans Wirel Commun, 2013, 12: 3412–3427

    Article  Google Scholar 

  7. 7

    Han C Z, Harrold T, Armour S, et al. Green radio: radio techniques to enable energy-efficient wireless networks. IEEE Commun Mag, 2011, 49: 46–54

    Article  Google Scholar 

  8. 8

    Ge X H, Tu S, Mao G Q, et al. 5G ultra-dense cellular networks. IEEE Wirel Commun, 2016, 23: 72–79

    Article  Google Scholar 

  9. 9

    Ge X H, Ye J L, Yang Y, et al. User mobility evaluation for 5G small cell networks based on individual mobility model. IEEE J Sel Areas Commun, 2016, 34: 528–541

    Article  Google Scholar 

  10. 10

    Miao G W, Himayat N, Li G Y. Energy-efficient link adaptation in frequency-selective channels. IEEE Trans Commun, 2010, 52: 545–554

    Article  Google Scholar 

  11. 11

    Auer G, Blume O, Giannini V, et al. Energy efficiency analysis of the reference systems, areas of improvements and target breakdown. Technical Report. EARTH Project. D2.3 V2

  12. 12

    Cui Q M, Cui Z Y, Zheng W, et al. Energy-aware deployment of dense heterogeneous cellular networks with QoS constraints. Sci China Inf Sci, 2017, 60: 042303

    Article  Google Scholar 

  13. 13

    Jin Y H, Qiu L, Liang X W. Small cells on/off control and load balancing for green dense heterogeneous networks. In: Proceedings of IEEE Wireless Communications and Networking Conference (WCNC), New Orleans, 2015. 1530–1535

    Google Scholar 

  14. 14

    Zhao X S, Wang C. An asymmetric cell selection scheme for inter-cell interference coordination in heterogeneous networks. In: Proceedings of IEEE Wireless Communications and Networking Conference (WCNC), Shanghai, 2013. 1226–1230

    Google Scholar 

  15. 15

    Sun X, Wang S W. Resource allocation scheme for energy saving in heterogeneous networks. IEEE Trans Wirel Commun, 2015, 14: 4407–4416

    Article  Google Scholar 

  16. 16

    Hossain E, Rasti M, Tabassum H, et al. Evolution toward 5G multi-tier cellular wireless networks: an interference management perspective. IEEE Wirel Commun, 2014, 21: 118–127

    Article  Google Scholar 

  17. 17

    Okino K, Nakayama T, Yamazaki C, et al. Pico cell range expansion with interference mitigation toward LTE- advanced heterogeneous networks. In: Proceedings of IEEE International Conference on Communications Workshops (ICC), Kyoto, 2011. 1–5

    Google Scholar 

  18. 18

    Bhushan N, Li J Y, Malladi D, et al. Network densification: the dominant theme for wireless evolution into 5G. IEEE Commun Mag, 2014, 52: 82–89

    Article  Google Scholar 

  19. 19

    Jo H-S, Sang Y J, Xia P, et al. Heterogeneous cellular networks with flexible cell association: a comprehensive downlink SINR analysis. IEEE Trans Wirel Commun, 2012, 11: 3484–3495

    Article  Google Scholar 

  20. 20

    Wu Y P, Cui Y, Clerckx B. Analysis and optimization of inter-tier interference coordination in downlink multi-antenna HetNets with offloading. IEEE Trans Wirel Commun, 2015, 14: 6550–6564

    Article  Google Scholar 

  21. 21

    Qin M L, Liu N, Jiang H L, et al. MPSO-based power adjustment and user association algorithm for energy efficiency in LTE heterogeneous networks. In: Proceedings of 6th International Conference on Wireless Communications and Signal Processing (WCSP), Hefei, 2014. 1–6

    Google Scholar 

  22. 22

    3GPP. 3rd Generation Partnership Project. Technical specification group radio access network; Further advancements for E-UTRA physical layer aspects (Release 9). Technical Specification 36.814 V9.0.0. 2010

    Google Scholar 

  23. 23

    Abuzainab N, Vinnakota S, Touati C. Coalition formation game for cooperative cognitive radio using Gibbs sampling. In: Proceedings of IEEE Wireless Communications and Networking Conference (WCNC), New Orleans, 2015. 937–942

    Google Scholar 

  24. 24

    Qian L P, Zhang Y J, Chiang M. Distributed nonconvex power control using Gibbs sampling. IEEE Trans Commun, 2012, 60: 3886–3898

    Article  Google Scholar 

  25. 25

    Garcia V, Chen C S, Zhou Y Q, et al. Gibbs sampling based distributed OFDMA resource allocation. Sci China Inf Sci, 2014, 57: 042302

    Article  Google Scholar 

  26. 26

    Liu F, Mahonen P, Petrova M. A handover scheme towards down-link traffic load balance in heterogeneous cellular networks. In: Proceedings of IEEE International Conference on Communications (ICC), Sydney, 2014. 4875–4880

    Google Scholar 

  27. 27

    Ye Q Y, Rong B Y, Chen Y D, et al. User association for load balancing in heterogeneous cellular networks. IEEE Trans Wirel Commun, 2013, 12: 2706–2716

    Article  Google Scholar 

  28. 28

    Jiang H L, Pan Z W, Liu N, et al. LD-IMPSO Based power adjustment algorithm for eICIC in QoS constrained hyper dense HetNets. Wirel Personal Commun, 2016, 88: 111–131

    Article  Google Scholar 

  29. 29

    Geman S, Geman D. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell, 1984, 6: 721–741

    Article  MATH  Google Scholar 

Download references


This research was supported by National Natural Science Foundation of China (Grant No. 61471114), Research Fund of the National Mobile Communications Research Laboratory, Southeast Univer- sity (Grant No. 2017A03), and Nature Research Fund for Key Project of Anhui Higher Education (Grant No. KJ2016A455).

Author information



Corresponding author

Correspondence to Pingping Xu.

Additional information

Conflict of interest The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhu, W., Xu, P., Bui, T. et al. Energy-efficient cell-association bias adjustment algorithm for ultra-dense networks. Sci. China Inf. Sci. 61, 022306 (2018).

Download citation


  • ultra-dense networks
  • cell-association bias
  • energy efficiency
  • Gibbs sampling
  • users’ data rate constraint