Wireless Personal Communications

, Volume 97, Issue 3, pp 3725–3742 | Cite as

Energy-Efficient Power Allocation for Multi-user Single-DF-Relay Networks

  • Shiguo WangEmail author
  • Xianru Liu


In wireless relay networks, energy efficiency not only affects the lifetime of mobile terminals, but also is a promising way to realize high-rate green communication by reducing transmission power and decreasing mutual interference. In this paper, for multi-user single-DF-relay cooperative networks, where the transmission power of all nodes are constrained and the direct links between sources and destinations are considered, the problem of optimal power allocation is formulated as how to solve a Lagrangian Function. Though it is difficult to get solution with Karush–Kuhn–Tucker (KKT) conditions directly, the solution of the Lagrangian Function is classified into two categories based on the analysis of Lagrangian Multipliers. Then, exact optimal power allocation strategies to minimize system-sum-power consumption are presented for both categories respectively. With the proposed scheme, not only all power constraints are satisfied, but also pre-determined target SNRs can be reached. Further numerical simulations are carried out to show the performance of the proposed strategies.


System-sum-power consumption Cooperative communication Multi-user single-relay Decode-and-forward(DF) Karush–Kuhn–Tucker(KKT) 



This work was supported by the Open Project Program of the Key Laboratory of Universal Wireless Communications (2016-KFKT-2016104), Ministry of Education, the Beijing University of Posts and Telecommunications, and the Natural Science Foundation of Hunan Province of China (2017JJ2249). And it was also funded by China Scholarship Council.


  1. 1.
    Sendonaris, A., Erkip, E., & Aazhang, B. (2003). User cooperation diversity—Part I: System description. IEEE Transactions on Communications, 51(11), 1927–1938.CrossRefGoogle Scholar
  2. 2.
    Sendonaris, A., Erkip, E., & Aazhang, B. (2003). User cooperation diversity—Part II: Implementation aspects and performance analysis. IEEE Transactions on Communications, 51(11), 1939–1948.CrossRefGoogle Scholar
  3. 3.
    Li, Q., Qian, Y., & Wu, G. (2012). Cooperative communicaitons for wireless networks: Techniques and applications in LTE-advanced systems. IEEE Wireless Communications, 19(2), 22–29.Google Scholar
  4. 4.
    Gomez-Cuba, F., Asorey-Cacheda, R., & Gonzalez-Castano, F. J. (2012). A survey on cooperative diversity for wireless networks. IEEE Communications Surveys & Tutorials, 14(3), 822–835. Third Quarter.Google Scholar
  5. 5.
    IEEE 802.16 Relay Task Group. The p802.16j baseline document for draft standard for local and metropolitan area networks. 802.16j-06/026r4, May (2007).Google Scholar
  6. 6.
    Further advancement for E-UTRA; Physical layer aspects. Sophia-Antipolis, France, 3GPP TR 36.814 V9.0.0, Release 9, Mar (2010).Google Scholar
  7. 7.
    Rangan, S., Rappaport, T. S., & Erkip, E. (2014). Millimeter-wave cellular wireless networks: Potentials and challenges. Proceedings of the IEEE, 102(3), 366–384.CrossRefGoogle Scholar
  8. 8.
    Hamouda, S., Chaabane, I. B., & Tabbane, S. (2015). Cooperative bandwidth sharing for relaying in LTE-advanced using game theory. IEEE Transactions on Vehicular Technology, 64(6), 2306–2317.CrossRefGoogle Scholar
  9. 9.
    Gao, C., Tang, J., Sheng, X., Zhang, W., & Wang, C. (2015). Greening wireless relay networks: An SNR-aware approach. IEEE Transactions on Parallel and Distributed Systems, 26(11), 3027–3039.CrossRefGoogle Scholar
  10. 10.
    Zhang, X., Xing, J., & Wang, W. (2013). Outage analysis of orthogonal space-time code transmission in cognitive relay networks with multiple antennas. IEEE Transactions on Vehicular Technology, 62(7), 3503–3509.CrossRefGoogle Scholar
  11. 11.
    Wang, S., & Ji, H. (2012). Distributed power allocation scheme for multi-relay shared-bandwidth(MRSB) wireless cooperative communiation. IEEE Communications Letters, 16(8), 1263–1265.CrossRefGoogle Scholar
  12. 12.
    Deng, X., & Haimovich, A. M. (2005). Power allocation for cooperative relaying in wireless networks. IEEE Communications Letters, 9(11), 994–996.CrossRefGoogle Scholar
  13. 13.
    Mo, Z., Su, W., & Batalama, S. (2014). Cooperative communication protocol designs based on optimum power and time allocation. IEEE Transactions on Wireless Communications, 13(8), 4283–4296.CrossRefGoogle Scholar
  14. 14.
    Gunduz, D., & Erkip, E. (2007). Opportunistic cooperation by dynamic resource allocation. IEEE Transactions on Wireless Communications, 6(4), 1446–1454.CrossRefGoogle Scholar
  15. 15.
    Naeem, M., Illanko, K., Karmokar, A., Anpalagan, A., & Jaseemunddin, M. (2014). Decode and forward relaying for energy-efficient multiuser cooperative cognitive radio network with outage constraints. IET Communications, 8(5), 578–586.CrossRefGoogle Scholar
  16. 16.
    Sheng, Z., Fan, J., Liu, C. H., Leung, V. C. M., Liu, X., & Leung, K. K. (2015). Energy-efficient relay selection for cooperative relaying in wireless multimedia networks. IEEE Transactions on Vehicular Technology, 64(3), 1156–1170.CrossRefGoogle Scholar
  17. 17.
    su, W., Sadek, A., & Liu, K. J. R. (2008). Cooperative communication protocols in wireless networks: Performance analysis and optimum power allocation. Wireless Personal Communications, 44(2), 181–217.CrossRefGoogle Scholar
  18. 18.
    Huang, X., & Ansari, N. Optimal cooperative power allocation for energy harvesting enabled relay networks. IEEE Transactions on Vehicular Technology. doi: 10.1109/TVT.2015.2424218.
  19. 19.
    Sokun, H. U., Sediq, A. B., Ikki, S., & Yanikomeroglu, H. (2015). Power allocation optimization in selective DF relaying with different modulationlevels in the presence of imperfect channel estmations. IEEE Communications Letters, 19(5), 867–870.CrossRefGoogle Scholar
  20. 20.
    Qian, L. P., Wu, Y., & Chen, Q. (2014). Transmit power minimization for outage-constrained relay selection over Rayleigh-fading channels. IEEE Communications Letters, 18(8), 1383–1386.CrossRefGoogle Scholar
  21. 21.
    Lin, J., Li, Q., Jiang, C., & , Shao, H. Joint multi-relay selection, power allocation and beamformer design for multi-user decode-and-forward relay networks. IEEE Transactions on Vehicular Technology. doi: 10.1109/TVT.2015.2462117.
  22. 22.
    Lin, J., Li, Q., Jiang, C.,&, Shao, H. Joint multi-relay selection, power allocation and beamformer design for multi-user decode-and-forward relay networks. IEEE Transactions on Vehicular Technology. doi: 10.1109/TVT.2015.2462117.
  23. 23.
    Devarajan, R., Jha, S. C., Phuyal, U., & KBhargava, V. (2012). Energy-aware resource allocation of cooperative cellular network using multi-objective optimization approach. IEEE Transactions on Wireless Communications, 11(5), 1797–1807.CrossRefGoogle Scholar
  24. 24.
    Gong, X., Vorobyov, S. A., & Tellambura, C. (2011). Joint bandwidth and power allocation with admission control in wireless multi-user networks with and without relaying. IEEE Transactions on Signal Processing, 59(4), 1801–1813.MathSciNetCrossRefGoogle Scholar
  25. 25.
    Vardhe, K., Reynolds, D., & woerner, B. D. (2010). Joint power allocation and relay selectionf or multiuser cooperative communication. IEEE Transactions on Wireless Communications, 9(4), 1255–1260.CrossRefGoogle Scholar
  26. 26.
    Phan, K. T., Le-Ngoc, T., Vorobyov, S. A., & Tellanmbura, C. (2009). Power allocation in wireless multi-user relay networks. IEEE Transactions on Wireless Communications, 8(5), 2535–2545.CrossRefGoogle Scholar
  27. 27.
    Ng, T. C.-Y., & Yu, W. (2007). Joint optimization of relay strategies and resource allocations in cooperative cellular networks. IEEE Journal on Selected Areas in Communications, 25(2), 328–339.CrossRefGoogle Scholar
  28. 28.
    Kim, I., & Kim, D. (2013). Outage-constrained source-sum-power minimization in multiple-sensor single-DF-relay networks. IEEE Communications Letters, 17(7), 1388–1391.CrossRefGoogle Scholar
  29. 29.
    Kim, I., & Kim, D. (2012). Source-sum-power minimizing in multi-sensor single-relay networks. IEEE Wireless Communications Letters, 16(7), 1076–1079.CrossRefGoogle Scholar
  30. 30.
    Wu, D., Cai, Y., & Guizani, M. (2014). Auction-based relay power allocation: Pareto optimality, fairness, and convergence. IEEE Transactions on Communications, 62(7), 2249–2259.CrossRefGoogle Scholar
  31. 31.
    Kim, I., & Kim, D. (2015). Minimizing operational power cost in remote-area wireless sensor networks with a DF relay and outage constraints. IEEE Communications Letters, 19(2), 247–250.CrossRefGoogle Scholar
  32. 32.
    Ruby, R., Leumng, V. C. M., & Michelson, D. (2015). Centralized and game theoretical solutions of joint source and relay power allocation for AF relay based network. IEEE Transactions on Communications, 63(8), 2848–2863.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Key Laboratory of Intelligent Computing and Information Processing (Xiangtan University), Ministry of EducationXiangtan UniversityXiangtanChina
  2. 2.School of Information Science and EngineeringCentral South UniversityChangshaChina

Personalised recommendations