Skip to main content
Log in

Fairness constrained diffusion adaptive power control for dense small cell network

  • Published:
Telecommunication Systems Aims and scope Submit manuscript

Abstract

Small cell is an emerging and promising technology for improving hotspots coverage and capacity, which tends to be densely deployed in populated areas. However, in a dense small cell network, the performances of users differ vastly due to the random deployments and the interferences. To guarantee fair performance among users in different cells, we propose a new distributed strategy for fairness constrained power control, referred to as the diffusion adaptive power control (DAPC). DAPC achieves overall network fairness in a distributed manner, in which each base station optimizes a local fairness with little information exchanged with neighboring cells. We study several adaptive algorithms to implement the proposed DAPC strategy. To improve the efficiency of the standard least mean square algorithm (LMS), we derive an adaptive step-size logarithm LMS algorithm, and discuss its convergence properties. Simulation results confirm the efficiency of the proposed methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Chandrasekhar, V., Andrews, J. G., & Gatherer, A. (2008). Femtocell networks: A survey. IEEE Communications Magazine, 46(9), 59–67.

    Article  Google Scholar 

  2. Andrews, J. G., Claussen, H., Dohler, M., Rangan, S., & Reed, M. C. (2012). Femtocells: Past, present, and future. IEEE Journal on Selected Areas in Communications, 30(3), 497–508.

    Article  Google Scholar 

  3. Abdelnasser, A., Hossain, E., & Kim, D. (2014). Clustering and resource allocation for dense femtocells in a two-tier cellular OFDMA network. IEEE Transactions on Wireless Communications, 13(3), 1628–1641.

    Article  Google Scholar 

  4. Pateromichelakis, E., Shariat, M., Quddus, A., Dianati, M., & Tafazolli, R. (2013). Dynamic clustering framework for multi-cell scheduling in dense small cell networks. IEEE Communications Letters, 17(9), 1802–1805.

    Article  Google Scholar 

  5. Cheung, W. C., Quek, T. Q. S., & Kountouris, M. (2012). Throughput optimization, spectrum allocation, and access control in two-tier femtocell networks. IEEE Journal on Selected Areas in Communications, 30(3), 561–574.

    Article  Google Scholar 

  6. Chu, X., Wu, Y., Lopez-Perez, D., & Tao, X. (2011). On providing downlink services in collocated spectrum-sharing macro and femto networks. IEEE Transactions on Wireless Communications, 10(12), 4306–4315.

    Article  Google Scholar 

  7. Chandrasekhar, V., Andrews, J., Muharemovict, T., Shen, Z., & Gatherer, A. (2009). Power control in two-tier femtocell networks. IEEE Transactions on Wireless Communications, 8(8), 4316–4328.

    Article  Google Scholar 

  8. Saad, M. (2011). Joint admission and power control for quality-of-service in the wireless downlink. Journal of Network and Computer Applications, 34(2), 644–652.

    Article  Google Scholar 

  9. Shahid, A., Aslam, S., Kim, H. S., & Lee, K. G. (2014). Distributed joint resource and power allocation in self-organized femtocell networks: A potential game approach. Journal of Network and Computer Applications, 46, 280–292.

    Article  Google Scholar 

  10. Guo, S., Dang, C., & Liao, X. (2011). Joint opportunistic power and rate allocation for wireless ad hoc networks: An adaptive particle swarm optimization approach. Journal of Network and Computer Applications, 34(4), 1353–1365.

    Article  Google Scholar 

  11. Karamad, E., Adve, R. S., & Chow, J. (2014). Scalable and efficient power control algorithms for wireless networks. IEEE Transactions on Signal Processing, 62(8), 2028–2041.

    Article  Google Scholar 

  12. Ngo, D. T., Le, L. B., & Le-Ngoc, T. (2012). Distributed pareto-optimal power control for utility maximization in femtocell networks. IEEE Transactions on Wireless Communications, 11(10), 2012.

    Article  Google Scholar 

  13. Lopez-Perez, D., Valcarce, A., de la Roche, G., & Zhang, J. (2009). Ofdma femtocells: A roadmap on interference avoidance. IEEE Communications Magazine, 47(9), 41–48.

    Article  Google Scholar 

  14. Claussen, H., Ho, L. T., & Samuel, L. G. (2008). Self-optimization of coverage for femtocell deployments. In Wireless Telecommunications Symposium, 2008. WTS 2008 (pp. 278-285). IEEE.

  15. Jung, H. B., & Kim, D. K. (2013). Power control of femtocells based on max–min fairness in heterogeneous networks. IEEE Communications Letters, 17(7), 1372–1375.

    Article  Google Scholar 

  16. 3GPP, Technical Report 36.921 (v11.0.0), “Home eNode B radio frequency requirements analysis,” Sept. 2012.

  17. Mo, J., & Walrand, J. (2000). Fair end-to-end window-based congestion control. IEEE/ACM Transactions on Networking, 8(5), 556–567.

    Article  Google Scholar 

  18. Hong, E. J., Yun, S. Y., & Cho, D.-H. (2009). Decentralized power control scheme in femtocell networks: A game theoretic approach. In 2009 IEEE 20th International Symposium on Personal, Indoor and Mobile Radio Communications (pp. 415–419).

  19. Al-Zahrani, A. Y., & Yu, F. R. (2016). An energy-efficient resource allocation and interference management scheme in green heterogeneous networks using game theory. IEEE Transactions on Vehicular Technology, 65(7), 5384–5396.

    Article  Google Scholar 

  20. Van Chien, T., Björnson, E., & Larsson, E. G. (2017). Joint pilot sequence design and power control for max–min fairness in uplink massive MIMO. arXiv preprint arXiv:1703.01916

  21. Guo, C., Liao, B., Huang, L., Zhang, P., Huang, M., & Zhang, J. (2016). On proportional fairness in power allocation for two-tone spectrum-sharing networks. IEEE Transactions on Vehicular Technology, 65(12), 10090–10096.

    Article  Google Scholar 

  22. Ji, H., & Huang, C.-Y. (1998). Non-cooperative uplink power control in cellular radio systems. Wireless Networks, 4(3), 233–240.

    Article  Google Scholar 

  23. Han, Z., & Liu, K. (2005). Noncooperative power-control game and throughput game over wireless networks. IEEE Transactions on Communications, 53(10), 1625–1629.

    Article  Google Scholar 

  24. Koskie, S., & Gajic, Z. (2005). A Nash game algorithm for sir-based power control in 3G wireless CDMA networks. IEEE/ACM Transactions on Networking, 13(5), 1017–1026.

    Article  Google Scholar 

  25. Rasti, M., Sharafat, A.-R., & Seyfe, B. (2009). Pareto-efficient and goal-driven power control in wireless networks: A game theoretic approach with a novel pricing scheme. IEEE/ACM Transactions on Networking, 17(2), 556–569.

    Article  Google Scholar 

  26. Li, W., Zheng, W., Su, T., & Wen, X. (2013). Distributed power control and pricing for two-tier OFMDA femtocell networks using fictitious game. In Wireless Communications and Networking Conference (WCNC), 2013 IEEE (pp. 470–475).

  27. Ma, Y., Lv, T., & Lu, Y. (2013). Efficient power control in heterogeneous femto-macro cell networks. In Wireless Communications and Networking Conference (WCNC), 2013 IEEE (pp. 4215–4219).

  28. Lopes, C., & Sayed, A. (2008). Diffusion least-mean squares over adaptive networks: Formulation and performance analysis. IEEE Transactions on Signal Processing, 56(7), 3122–3136.

    Article  Google Scholar 

  29. Hatoum, A., Aitsaadi, N., Langar, R., Boutaba, R., & Pujolle, G. (2011). FCRA: Femtocell cluster-based resource allocation scheme for ofdma networks. In 2011 IEEE International Conference on Communications (ICC) (pp. 1–6).

  30. Widrow, B., & Stearns, S. D. (1985). Adaptive signal processing. Englewood Cliffs: Prentice-Hall PTR.

    Google Scholar 

  31. Liu, Y.-F., Dai, Y.-H., & Luo, Z.-Q. (2013). Joint power and admission control via linear programming deflation. IEEE Transactions on Signal Processing, 61(6), 1327–1338.

    Article  Google Scholar 

  32. Jain, R., Durresi, A., & Babic, G. (1999). Throughput fairness index: An explanation. ATM Forum/99-0045.

  33. Femto-Forum. (2010). Interference management in OFDMA femtocells. In femtoforum.

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 61372092 and “863” Fund under Grants 2014AA01A701

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhirong Luan.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Appendix

Appendix

1.1 Proof of (13)

We define the transmit power in dB, \(p\_dB_{FAP_{i,t} } \), as

$$\begin{aligned} p\_dB_{FAP_{i,t} } =10\log p_{FAP_i ,t} \end{aligned}$$
(A-1)

Since the update is in logarithm, the gradient should also be changed as the gradient of \(p\_dB_{FAP_{i,t} } \).

$$\begin{aligned} p\_dB_{FAP_{i,t+1} }= & {} p\_dB_{FAP_{i,t} }\nonumber \\&+\, \mu _i \left( -\frac{dF_{FAP_i ,t} }{dp\_dB_{FAP_{i,t} } }\right) \end{aligned}$$
(A-2)
$$\begin{aligned} \Rightarrow \quad p\_dB_{FAP_{i,t+1} }= & {} p\_dB_{FAP_{i,t} } \nonumber \\&+\, \mu _i \left( -\frac{dF_{FAP_i ,t} }{dp_{FAP_{i,t} } }\frac{dp_{FAP_{i,t} } }{dp\_dB_{FAP_{i,t} } }\right) \nonumber \\ \end{aligned}$$
(A-3)
$$\begin{aligned} \Rightarrow \quad p\_dB_{FAP_{i,t+1} }= & {} p\_dB_{FAP_{i,t} }\nonumber \\&+\, \mu _i \underbrace{\left( -\frac{dF_{FAP_i ,t} }{dp_{FAP_{i,t} } }\frac{p_{FAP_{i,t} } }{10}\ln 10\right) }_{gradient} \nonumber \\ \end{aligned}$$
(A-4)

where \(\mu \) is a fixed value and \(\frac{10}{p_{FAP_{i,t} } \ln 10}\) is always positive. In this way, the update is adaptive step-size and it is redefined as

$$\begin{aligned} 10\log p_{FAP_i ,t+1} =10\log p_{FAP_i ,t} +\mu \left( {-\frac{dF_{FAP_i ,t} }{dp_{FAP_{i,t} } }} \right) \nonumber \\ \end{aligned}$$
(A-5)

which completes the proof. \(\square \)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Luan, Z., Qu, H., Zhao, J. et al. Fairness constrained diffusion adaptive power control for dense small cell network. Telecommun Syst 68, 373–384 (2018). https://doi.org/10.1007/s11235-017-0387-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11235-017-0387-z

Keywords

Navigation