Skip to main content
Log in

Distributed SNR-Based Power Allocation in Wireless Parallel Amplify-and-Forward Relay Transmissions Using Cournot Game

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

In wireless communications, power allocation plays a paramount role in sustainable network lifetime prolongation with quality-of-service and network interference reduction. This paper investigates a distributed power allocation problem in wireless parallel amplify-and-forward (AF) relay transmissions. Particularly, the objective is set to minimize the total transmit power while guaranteeing the signal-to-noise ratio (SNR) requirement at the destination node. The distributed SNR-based power allocation problem is formulated and modeled as a Cournot game. Moreover, a distributed SNR-based power allocation algorithm is proposed to solve the Cournot game. The proposed distributed SNR-based power allocation algorithm is proved to converge to a unique equilibrium. To evaluate the distributed method, a centralized optimal SNR-based power allocation algorithm is also proposed. Numerical results show that the proposed distributed SNR-based power allocation algorithm can achieve comparable performance to the centralized optimal SNR-based power allocation algorithm.

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

Similar content being viewed by others

References

  1. Xia B., Wang J. (2005) Effect of channel-estimation error on QAM systems with antenna diversity. IEEE Transactions on Communications 53(3): 481–488

    Article  Google Scholar 

  2. Wang X., Wang J. (2004) Effect of imperfect channel estimation on transmit diversity in CDMA systems. IEEE Transactions on Vehicular Technology 53(5): 1400–1412

    Article  Google Scholar 

  3. IEEE 802.16m. (2011). IEEE standard for local and metropolitan area networks-Part 16: Air interface for broadband wireless access systems: Advanced air interface.

  4. 3GPP TR 36.813 V0.1.1. (2008). Future advancements for E-UTRA, physical layer aspects.

  5. van der Meulen E. C. (1971) Three-terminal communication channels. Advances in Applied Probability 3(1): 120–154

    Article  MathSciNet  MATH  Google Scholar 

  6. Cover T. M., Gamal A. A. El. (1979) Capacity theorems for the relay channel. IEEE Transactions on Information Theory IT-25(5): 572–584

    Article  Google Scholar 

  7. Farhadi G., Beaulieu N. (2008) On the ergodic capacity of wireless relaying systems over rayleigh fading channels. IEEE Transactions on Wireless Communications 7(11): 4462–4467

    Article  Google Scholar 

  8. Ding Y., Zhang J. K., Wong K. M. (2009) Ergodic channel capacities for the amplify-and-forward half-duplex cooperative systems. IEEE Transactions on Information Theory 55(2): 713–730

    Article  MathSciNet  Google Scholar 

  9. Kwon U.-K., Choi C.-H., Im G.-H. (2009) Full-rate cooperative communications with spatial diversity for half-duplex uplink relay channels. IEEE Transactions on Wireless Communications 8(11): 5449–5454

    Article  Google Scholar 

  10. Zhao X., Wang J.-B., Wang J.-Y., Chen M., Feng M., Sheng M. (2011) System outage probability analysis in unlink multi-hop cellular systems over composite channels. EURASIP Journal on Wireless Communications and Networking 2011(1): 35

    Article  Google Scholar 

  11. Ding Z., Leung K. K., Goeckel D. L., Towsley D. (2009) On the study of network coding with diversity. IEEE Transactions on Wireless Communications 8(3): 1247–1259

    Article  Google Scholar 

  12. Luo J., Blum R. S., Cimini L. J., Greenstein L. J., Haimovich A. M. (2007) Decode-and-forward cooperative diversity with power allocation in wireless networks. IEEE Transactions on Wireless Communications 6(3): 793–799

    Article  Google Scholar 

  13. 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

    Article  Google Scholar 

  14. Host-Madsen A., Zhang J. (2005) Capacity bounds and power allocation for wireless relay channels. IEEE Transactions on Information Theory 51(6): 2020–2040

    Article  MathSciNet  Google Scholar 

  15. Madan, R., Mehta, N. B., Molisch, A. F., & Zhang, J. (2006). Energy-efficient cooperative relaying over fading channels with simple relay selection. In IEEE Global Telecommnications Conference. San Francisco: IEEE.

  16. Seddik K. G., Sadek A. K., Su W., Liu K. J. R. (2007) Outage analysis and optimal power allocation for multimode relay networks. IEEE Signal Processing Letters 14(6): 377–380

    Article  Google Scholar 

  17. Brown, D. R., III. (2004). Resource allocation for cooperative transmission in wireless networks with orthogonal users. In The 38th Asilomar conference on signals, systems and computers (pp. 1473–1477). California: IEEE.

  18. Cai J., Shen X., Mark Joh. W. (2008) Semi-distributed user relaying algorithm for amplify-and-forward wireless relay networks. IEEE Transactions on Wireless Communications 7(4): 1348–1357

    Article  Google Scholar 

  19. Chen M., Yener A. (2008) Distributed power allocation strategies for parallel relay networks. IEEE Transactions on Wireless Communications 7(2): 552–561

    Article  Google Scholar 

  20. Ma Y., Yi N., Tagazolli R. (2008) Bit and power loading for OFDM-Based three-node relaying communications. IEEE Transactions on Signal Processing 56(7): 3236–3247

    Article  MathSciNet  Google Scholar 

  21. Phan, K. T., Le, L. B., Vorobyov, S. A., & Tho, L.-N. (2009). Centralized and distributed power allocation in multi-user wireless relay networks. In IEEE international conference on communications. Dresden: IEEE.

  22. Yu W., Ginis G., Cioffi J. (2002) Distributed multiuser power control for digital subscriber lines. IEEE Journal on Selected Areas in Communications 20(5): 1105–1115

    Article  Google Scholar 

  23. Agustin, A., Munoz, O., & Vidal, J. (2004). A game theoretic approach for cooperative MIMO systems with cellular reuse of the relay slot. In IEEE international conference on acoustics, speech, and signal processing (pp. 581–584). Montreal: IEEE.

  24. Huang J., Han Z., Chiang M., Poor H. V. (2008) Auction-based resource allocation for cooperative communications. IEEE Journal on Selected Areas in Communications 26(7): 1226–1237

    Article  Google Scholar 

  25. Shi Y., Wang J., Letaief K. B., Mallik R. (2009) A game-theoretic approach for distributed power control in interference relay channels. IEEE Transactions on Wireless Communications 8(6): 3151–3161

    Article  Google Scholar 

  26. Ren S., Schaar M. (2010) Distributed power allocation in multi-user multi-channel cellular relay networks. IEEE Transactions on Wireless Communications 9(6): 1952–1964

    Article  Google Scholar 

  27. Wang B., Han Z., Liu K. J. R. (2009) Distributed relay selection and power control for multiuser cooperative communication networks using Stackelberg Game. IEEE Transactions on Mobile Computing 8(7): 975–990

    Article  Google Scholar 

  28. Yu, X., Wu, T., Huang, J., & Wang, Y. (2008). A non-cooperative game approach for distributed power allocation in multi-cell OFDMA-relay networks. In IEEE vehicular technology conference (pp. 1920–1924). Marina Bay: IEEE.

  29. Colander D. C. (2008) Microeconomics (7th ed.). McGraw-Hill, New York

    Google Scholar 

  30. Tirole J. (1998) The theory of industrial organization. MIT Press, Cambridge

    Google Scholar 

  31. Saraydar C. U., Mandayam N. B., Goodman D. J. (2002) Efficient power control via pricing in wireless data networks. IEEE Transactions on Communications 50(2): 291–303

    Article  Google Scholar 

  32. Rosen J. B. (1965) Existence and uniqueness of equilibrium points forconcave N-person Games. Econometrica 33(3): 520–534

    Article  MathSciNet  MATH  Google Scholar 

  33. Droste E., Hommes E., Tuinstra J. (2002) Endogenous fluctuations under evolutionary pressure in Cournot competition. Games and Economic Behavior 40(2): 232–269

    Article  MathSciNet  MATH  Google Scholar 

  34. Theocharis R. D. (1960) On the stability of the Cournot solution on the oligopoly problem. Review of Economic Studies 27(2): 133–134

    Article  Google Scholar 

  35. Thorlund-Petersen L. (1990) Iterative computation of Cournot equilibrium. Games and Economic Behavior 2(1): 61–75

    Article  MathSciNet  MATH  Google Scholar 

  36. Yates R. D. (1995) A framework for uplink power control in cellular radio systems. IEEE Journal on Selected Areas in Communications 13(7): 1341–1347

    Article  MathSciNet  Google Scholar 

  37. Press W. H., Flamery B. P., Teukolsky S. A., Vetterling W. T. (1992) Numerical recipes in C. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  38. Sundaram R. K. (1996) A first course in optimization theory. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  39. UMTS 30. 03. (1998). Annex B: test environments and deployment models.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jun-Bo Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, JB., Wang, JY., Song, X. et al. Distributed SNR-Based Power Allocation in Wireless Parallel Amplify-and-Forward Relay Transmissions Using Cournot Game. Wireless Pers Commun 70, 1285–1306 (2013). https://doi.org/10.1007/s11277-012-0747-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-012-0747-7

Keywords

Navigation