Skip to main content
Log in

A fully distributed learning algorithm for power allocation in heterogeneous networks

Computing Aims and scope Submit manuscript

Cite this article


In this work, we present a fully distributed Learning algorithm for power allocation in HetNets, referred to as the FLAPH, that reaches the global optimum given by the total social welfare. Using a mix of macro and femto base stations, we discuss opportunities to maximize users global throughput. We prove the convergence of the algorithm and compare its performance with the well-established Gibbs and Max-logit algorithms which ensure convergence to the global optimum. Algorithms are compared in terms of computational complexity, memory space, and time convergence.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4


  1. Ghosh A, Ratasuk R, Mondal B, Mangalvedhe N, Thomas T (2010) LTE-advanced: next-generation wireless broadband technology. IEEE Wirel Commun 17(3):10–22

    Article  Google Scholar 

  2. Advanced Wireless Technology Group (AWTG) (2013) Heterogeneous networks (HetNets) using small cells. White paper

  3. Darmann A, Pferschy U, Schauer J (2010) Resource allocation with time intervals. Theor Comput Sci 411(49):4217–4234

    Article  MathSciNet  MATH  Google Scholar 

  4. Adeane J, Rodrigues MRD, Wassell IJ (2005) Centralized and distributed power allocation algorithms in cooperative networks. In: IEEE 6th international workshop on signal processing advances in wireless communications (SPAWC), New York, pp 333–337

  5. Li J, Chen X, Botella C, Svensson T, Eriksson T (2012) Resource allocation for OFDMA systems with multi-cell joint transmission. In: IEEE 13th international workshop on signal processing advances in wireless communications (SPAWC), Cesme, pp 179–183

  6. Li J, Svensson T, Botella C, Eriksson T, Xu X, Chen X (2012) Joint scheduling and power control in coordinated multi-point clusters. In: IEEE vehicular technology conference (VTC Fall), Yokohama, pp 1–5

  7. Kauffmann B, Baccelli F, Chaintreau A, Mhatre V, Papagiannaki K, Diot C (2007) Measurement-based self organization of interfering 802.11 wireless access networks. In: 26th IEEE international conference on computer communications (INFOCOM), Anchorage, pp 1451–1459

  8. Chen C, Baccelli F (2010) Self-optimization in mobile cellular networks: power control and user association. In: IEEE international conference on communications (ICC), Cape Town, pp 1–6

  9. Borst S, Markakis M, Saniee I (2011) Distributed power allocation and user assignment in OFDMA cellular networks. In: The annual conference on communication, control, and computing, Allerton Park, pp 46–64

  10. Bertsimas D, Tsitsiklis J (1993) Simulated annealing. Stat Sci 8(1):10–15

    Article  MATH  Google Scholar 

  11. Hajek B (1988) Cooling schedules for optimal annealing. Math Oper Res 13(2):311–329

    Article  MathSciNet  MATH  Google Scholar 

  12. Song Y, Wong SHY, Lee K (2011) A Game theoretical approach to gateway selections in multi-domain wireless networks. In: Proceedings of the fifth annual conference of the international technology alliance

  13. Xing Y, Maille P, Tuffin B, Chandramouli R (2009) User strategy learning when pricing a red buffer. Simul Model Pract Theor 17:548–557

    Article  Google Scholar 

  14. Raghunathan V, Kumar P (2004) On delay-adaptive routing in wireless networks. In: 44th IEEE conference on decision and control (CDC), Seville, pp 4661–4666

  15. Tuffin B, Maille P (2006) How many parallel TCP sessions to open: a pricing perspective. In: ICQT 2006. LNCS, vol 4033. Springer, Heidelberg, pp 2–12

  16. Barth D, Echabbi L, Hamlaoui C (2008) Optimal transit price negotiation: the distributed learning perspective. J Univ Comput Sci 14(5):745–765

    Google Scholar 

  17. Xing Y, Chandramouli R (2008) Stochastic learning solution for distributed discrete power control game in wireless data networks. IEEE ACM Trans Netw 16(4):932–944

    Article  Google Scholar 

  18. Shannon CE (1949) Communication in the presence of noise. In: Proceedings of the institute of radio engineers, pp 10–21

  19. Borst S, Markakis M, Saniee I (2013) Nonconcave utility maximization in locally coupled systems, with applications to wireless and wireline networks. IEEE ACM Trans Netw 22(2):674–687

    Article  Google Scholar 

  20. Ahmed Khan M, Tembine H, Vasilakos AV (2012) Game dynamics and cost of learning in heterogeneous 4G networks. IEEE J Sel Areas Commun 30(1):198–213

    Article  Google Scholar 

  21. Hastings WK (1970) Monte carlo sampling methods using markov chains and their applications. Biometrika 57(1):97–109

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Hajar El Hammouti.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

El Hammouti, H., Echabbi, L. & El Azouzi, R. A fully distributed learning algorithm for power allocation in heterogeneous networks. Computing 101, 1287–1303 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


Mathematics Subject Classification