Multi-relay selection in energy-harvesting cooperative wireless networks: game-theoretic modeling and analysis

  • Mohammed W. BaidasEmail author
  • Emad Alsusa
  • Motasem Alfarra
  • Mubarak Al-Mubarak


This paper studies distributed multi-relay selection in energy-harvesting cooperative wireless networks and models it as an Indian Buffet Game (IBG). Particularly, the IBG is utilized to model the multi-relay selection decisions of network source nodes, while accounting for negative network externality. Two scenarios are considered: (1) constrained selections (CS), and (2) unconstrained selections (US). In the former scenario, each source is constrained to a maximum number of relay selections; while in the latter scenario, the source nodes can select as many relays as possible. Since the relays are energy-harvesting—and thus intermittently harvest random amounts of energy—the accumulated energy at each relay is unknown to the source nodes, leading to uncertain relays’ energy states. In turn, a non-Bayesian learning (NBL) algorithm is devised for the source nodes to learn the relays’ energy states. After that, two distributed best-response (BR) recursive algorithms, namely BR-CS and BR-US, are proposed to allow the source nodes to make multi-relay selection decisions, while guaranteeing subgame perfect Nash equilibrium. Simulation results are presented to verify the efficacy of the proposed distributed NBL and multi-relay selection algorithms. Specifically, the NBL is shown to efficiently learn the true relays’ energy states. More importantly, the BR-CS algorithm is shown to be comparable to the centralized multi-relay selection—and superior to other relay selection schemes—in terms of network sum-rate improvement (and utility). Lastly, the number of relay selections of the BR-CS algorithm must be constrained to the minimum so as to reduce complexity and fully exploit diversity gains.


Cooperation Distributed Energy-harvesting Game theory Learning Multi-relay selection 



  1. 1.
    Lu, X., Wang, P., Niyato, D., & Han, Z. (2015). Wireless networks with RF energy harvesting: A contemporary survey. IEEE Communications Surveys and Tutorials, 17(2), 757–789.CrossRefGoogle Scholar
  2. 2.
    Ulukus, S., Yener, A., Erkip, E., Simeone, O., Zorzi, M., Grover, P., et al. (2015). Energy harvesting wireless communications: A review of recent advances. IEEE Journal on Selected Areas in Communications, 33(3), 360–381.CrossRefGoogle Scholar
  3. 3.
    Liu, K. J. R., Sadek, A. K., Su, W., & Kwasinski, A. (2008). Cooperation communications and networking. New York: Cambridge University Press.CrossRefGoogle Scholar
  4. 4.
    Baidas, M. W. (2014). Cooperation in wireless networks: A game-theoretic framework with reinforcement learning. IET Communications, 8(5), 740–753.CrossRefGoogle Scholar
  5. 5.
    Bahbahani, M. S., Baidas, M. W., & Alsusa, E. (2015). A distributed political coalition formation framework for multi-relay selection in cooperative wireless networks. IEEE Transactions on Wireless Communications, 14(12), 6869–6882.CrossRefGoogle Scholar
  6. 6.
    Bahbahani, M. S., & Alsusa, E. (2016). Joint cost-sharing and multi-relay selection for two-way networks using a pricing game. In Proceedings of IEEE wireless communications and networking conference (WCNC) (pp. 1–6).Google Scholar
  7. 7.
    Bahbahani, M. S., & Alsusa, E. (2016). Relay selection for energy harvesting relay networks using a repeated game. In Proceedings of IEEE wireless communications and networking conference (WCNC) (pp. 1–6).Google Scholar
  8. 8.
    Baidas, M. W., & Bahbahani, M. S. (2016). Game-theoretic modeling and analysis of relay selection in cooperative wireless networks. Wireless Communications and Mobile Computing, 16(5), 500–518.CrossRefGoogle Scholar
  9. 9.
    Ding, L., Shen, L., Liu, D., Xu, K., & Xu, Y. (2017). A game theoretic learning solution for distributed relay selection on throughput maximization. Wireless Networks, 23(6), 1757–1766.CrossRefGoogle Scholar
  10. 10.
    Baidas, M. W., & Alsusa, E. (2016). Power allocation, relay selection, and energy cooperation strategies in energy harvesting cooperative wireless networks. Wireless Communications and Mobile Computing, 16(4), 2065–2082.CrossRefGoogle Scholar
  11. 11.
    Yang, D., Zhu, C., Xiao, L., Shen, X., & Zhang, T. (2016). An energy-efficient scheme for multirelay cooperative networks with energy harvesting. Mobile Information Systems, 2016, Article ID 5618935. Scholar
  12. 12.
    Do, N. T., Bao, V. N. Q., & An, B. (2016). Outage performance analysis of relay selection schemes in wireless energy harvesting cooperative networks over non-identical Rayleigh fading channels. Sensors, 16(3), 295.CrossRefGoogle Scholar
  13. 13.
    Do, N. T., Bao, V. N. Q., & An, B. (2015). A relay selection protocol for wireless energy harvesting relay networks. In Proceedings of IEEE international conference on advanced technologies for communications (ATC) (pp. 243–247).Google Scholar
  14. 14.
    Son, P. N., & Kong, H. Y. (2015). Energy-harvesting relay selection schemes for decode-and-forward dual-hop networks. IEICE Transactions on Communications, 98(12), 2485–2495.CrossRefGoogle Scholar
  15. 15.
    Gu, Y., Chen, H., Li, Y., Liang, Y., & Vucetic, B. (2017). Distributed multi-relay selection in accumulate-then-forward energy harvesting relay networks. IEEE Transactions on Green Communications and Networking, 2(1), 74–86.CrossRefGoogle Scholar
  16. 16.
    Zheng, L., Zhai, C., & Liu, J. (2018). Alternate energy harvesting and information relaying in cooperative AF networks. Telecommunication Systems, 68(3), 523–533.CrossRefGoogle Scholar
  17. 17.
    Song, X., Xu, S., Xie, Z., & Han, X. (2019). Joint optimal power allocation and relay selection scheme in energy-harvesting two-way relaying networks. Future Internet, 11, 47. Scholar
  18. 18.
    Nguyen, T. N., Minh, T. H. Q., Tran, P. T., Voznak, M., Duy, T. T., Nguyen, T.-L., et al. (2019). Performance enhancement for energy harvesting based two-way relay protocols in wireless ad-hoc networks with partial and full relay selection methods. Ad Hoc Networks, 84(1), 178–187.CrossRefGoogle Scholar
  19. 19.
    Bao, V. N. Q., & Van, N. T. (2018). Incremental relaying networks with energy harvesting relay selection: Performance analysis. Emerging Telecommunications Technologies, 29(12), e3483.CrossRefGoogle Scholar
  20. 20.
    Andrawes, A., Nordin, R., & Ismail, M. (2019). Wireless energy harvesting with cooperative relaying under the best relay selection scheme. Energies, 12(5), 892. Scholar
  21. 21.
    Jiang, C., Chen, Y., Gao, Y., & Liu, K. J. R. (2015). Indian buffet game with negative network externality and non-bayesian social learning. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 45(4), 609–623.CrossRefGoogle Scholar
  22. 22.
    Griffiths, T. L., & Ghahramani, Z. (2011). The Indian buffet process: An introduction and review. Journal of Machine Learning, 12, 1185–1224.Google Scholar
  23. 23.
    Zhang, Y., Pan, E., Song, L., Saad, W., Dawy, Z., & Han, Z. (2015). Social network aware device-to-device communication in wireless networks. IEEE Transactions on Wireless Communications, 14(1), 177–190.CrossRefGoogle Scholar
  24. 24.
    Hung, H. J., Ho, T. Y., Lee, S. Y., Yang, C. Y., & Yang, D. N. (2018). Relay selection for heterogeneous cellular networks with renewable green energy sources. IEEE Transactions on Mobile Computing, 17(3), 661–674.CrossRefGoogle Scholar
  25. 25.
    Lee, S. Y., Liu, C. Y., Chang, M. K., Yang, D. N., & Hong, Y. W. P. (2016). Cooperative multicasting in renewable energy enhanced relay networks—Expending more power to save energy. IEEE Transactions on Wireless Communications, 15(1), 753–768.CrossRefGoogle Scholar
  26. 26.
    Zhe, W., Wang, X., Aldiab, M., & Jaber, T. (2015). User association for energy harvesting relay stations in cellular networks. EURASIP Journal on Wirless Communications and Networking, 264, 1–12.Google Scholar
  27. 27.
    Miridakis, N. I., Tsiftsis, T. A., Alexandropolous, G. C., & Debbah, M. (2016). Green cognitive relaying: Opportunistically switching between data transmission and energy harvesting. IEEE Journal on Selected Areas in Communications, 34(12), 3725–3738.CrossRefGoogle Scholar
  28. 28.
    Renyi, A. (1970). Probability theory. Amsterdam: North-Holland.Google Scholar
  29. 29.
    Buonocore, A., Pirozzi, E., & Caputo, L. (2009). A note on the sum of uniform random variables. Elsevier Statistics and Probability Letters, 79(10), 2092–2097.CrossRefGoogle Scholar
  30. 30.
    Ross, S. M. (2009). Introduction to probability models (10th ed.). London: Academic Press.Google Scholar
  31. 31.
    Tsao, C. K. (1956). Distribution of the sum in random samples from a discrete population. Annals of Mathematical Statistics, 27(3), 703–712.CrossRefGoogle Scholar
  32. 32.
    Adelson, R. M. (1966). Compound poisson distributions. Operations Research, 17(1), 73–75.CrossRefGoogle Scholar
  33. 33.
    Baidas, M. W., & MacKenzie, A. B. (2014). Many-to-many space-time network coding for amplify-and-forward cooperation networks: Node selection and performance analysis. EURASIP Journal on Wireless Communications and Networking, 48, 1–7. Scholar
  34. 34.
    Baidas, M. W., & MacKenzie, A. B. (2011). Auction-based power allocation for many-to-one cooperative wireless networks. In Proceedings of IEEE international wireless communications and mobile computing conference, (pp. 1677–1682).Google Scholar
  35. 35.
    Osborne, J. (2003). An introduction to game theory. New York: Oxford University Press.Google Scholar
  36. 36.
    Bonami, P., Kilinc, M., & Linderoth, J. (2012). Algorithms and software for convex mixed integer nonlinear programs. The IMA Volumes in Mathematics and its Applications, 154, 1–39.CrossRefGoogle Scholar
  37. 37.
    Nowak, L. (2005). Relaxation and decomposition methods for mixed integer nonlinear programming. Basel: Springer.Google Scholar
  38. 38.
    Schlueter, M. (2014). MIDACO software performance on interplanetary trajectory benchmarks. Advances in Space Research, 54(4), 744–754.CrossRefGoogle Scholar
  39. 39.
    Zhao, Y., Adve, R., & Lim, T. (2007). Improving amplify-and-forward relay networks: Optimal power allocation versus selection. IEEE Transactions on Wireless Communications, 6(8), 3114–3123.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019
corrected publication 2019

Authors and Affiliations

  1. 1.Department of Electrical Engineering, College of Engineering and PetroleumKuwait UniversityKuwait CityKuwait
  2. 2.School of Electrical and Electronic EngineeringUniversity of ManchesterManchesterUK
  3. 3.Department of Electrical EngineeringKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  4. 4.Department of Electrical and Computer EngineeringOhio State UniversityColumbusUS

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