Skip to main content

Advertisement

SpringerLink
Log in

Game theoretic power allocation for fading MIMO multiple access channels with imperfect CSIR

  • Published:
Telecommunication Systems Aims and scope Submit manuscript

Abstract

In this paper, we formulate the power allocation (PA) problem for uplink of MIMO fading multiple access channels using a game theoretic framework with channel estimation error at receiver side. We investigate the effect of the error on derived PA policy and on performance of the system. Furthermore, it is assumed that the CSI at transmitter side is imperfect i.e., each transmitter is informed with the statistics of the channels instead of the instantaneous channel states. We use lower bound of mutual information between each user and the base station to derive a utility function for the concave game, regarding the channel estimation error. Following the formulation of problem, existence and uniqueness of the game’s equilibrium are investigated and it is proved that the proposed game has a unique Nash equilibrium (NE). Also a primal-dual subgradient based best-response algorithm is designed to find the NE. The algorithm updates the policy of each player regarding the given policy of other players, at each iteration. Finally, simulation results of the achieved PA policy are illustrated to investigate the effect of channel estimation error. In particular, simulations show that the overall system performance will be improved when channel estimation error in modeling the PA game is considered.

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

Access this article

Log in via an institution

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
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Jarmyr, S., Ottersten, B., & Jorswieck, E. A. (2014). Statistical framework for optimization in the multi-user MIMO uplink with ZF-DFE. IEEE Transactions on Signal Processing, 62(10), 2730–2745.

    Article  Google Scholar 

  2. Miao, G. (2013). Energy-efficient uplink multi-user MIMO. IEEE Transactions on Wireless Communications, 12(5), 2302–2313.

    Article  Google Scholar 

  3. Soysal, A., & Ulukus, S. (2007). Optimum power allocation for single-user MIMO and multi-user MIMO-MAC with partial CSI. IEEE Journal on Selected Areas in Communications, 25(7), 1402–1412.

    Article  Google Scholar 

  4. Yoo, T., & Goldsmith, A. (2006). Capacity and power allocation for fading MIMO channels with channel estimation error. IEEE Transactions on Information Theory, 52(5), 2203–2214.

    Article  Google Scholar 

  5. Belmega, E. V. (2010). On resource allocation problem in distributed MIMO wireless networks, Ph.D. Dissertation, Joint lab of CNRS., Suplec.

  6. Telatar, E. (1999). Capacity of multiantenna Gaussian channels. European Transactions on Telecommunications, 10(6), 585–595.

    Article  Google Scholar 

  7. Yu, W., Rhee, W., Boyd, S., & Cioffi, J. M. (2004). Iterative water-filling for Gaussian vector multiple-access channels. IEEE Transactions on Information Theory, 50(1), 145–152.

    Article  Google Scholar 

  8. Cirik, A., Rong, Y., & Hua, Y. (2014). Achievable rates of full-duplex MIMO radios in fast fading channels with imperfect channel estimation. IEEE Transactions on Signal Processing, 62(15), 3874–3886.

    Article  Google Scholar 

  9. Goldsmith, A., Jafar, S. A., Jindal, N., & Vishwanath, S. (2003). Capacity limits of MIMO channels. IEEE Journal on Selected Areas in Communications, 21(5), 684–702.

    Article  Google Scholar 

  10. Zheng, L., & Tse, D. N. C. (2002). Communication on the Grassmann manifold: A geometric approach to the noncoherent multiple-antenna channel. IEEE Transactions on Information Theory, 48(2), 359–383.

    Article  Google Scholar 

  11. Hassibi, B., & Hochwald, B. M. (2003). How much training is needed in multiple-antenna wireless links? IEEE Transactions on Information Theory, 49(4), 951–963.

    Article  Google Scholar 

  12. Baltersee, J., Fock, G., & Meyr, H. (2001). Achievable rate of MIMO channels with data-aided channel estimation and perfect interleaving. IEEE Journal on Selected Areas in Communications, 19(12), 2358–2368.

    Article  Google Scholar 

  13. Musavian, L., & Aissa, S. (2008). On the achievable sum-rate of correlated mimo multiple access channel with imperfect channel estimation. IEEE Transactions on Wireless Communications, 7(7), 2549–2559.

    Article  Google Scholar 

  14. Cover, T. M., & Thomas, J. A. (2012). Elements of information theory. New York: Wiley.

    Google Scholar 

  15. Ding, Z., Perlaza, S. M., Esnaola, I., & Poor, H. V. (2014). Power allocation strategies in energy harvesting wireless cooperative networks. IEEE Transactions on Wireless Communications, 13(2), 846–860.

    Article  Google Scholar 

  16. Guruacharya, S., Niyato, D., Kim, D. I., & Hossain, E. (2013). Hierarchical competition for downlink power allocation in OFDMA femtocell networks. IEEE Transactions on Wireless Communications, 12(4), 1543–1553.

    Article  Google Scholar 

  17. Grandhi, S. A., Vijayan, R., & Goodman, D. (1994). Distributed power control in cellular radio systems. IEEE Transactions on Communications, 42(234), 226–228.

    Article  Google Scholar 

  18. Lasaulce, S., Suarez, A., Debbah, M., & Cottatellucci, L. (2007). Power allocation game for fading MIMO multiple access channels with antenna correlation. In: Proceedings of the ACM International Conference on Game Theory in Communication Networks (Gamecomm), vol. 19, Nantes.

  19. Belmega, E. V., Lasaulce, S., & Debbah, M. (2009). Power allocation games for MIMO multiple access channels with coordination. IEEE Transactions on Wireless Communications, 8(6), 3182–3192.

    Article  Google Scholar 

  20. Tembine, H. (2011). Dynamic robust games in mimo systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 41(4), 990–1002.

    Article  Google Scholar 

  21. Bertsekas, D. P. (2009). Convex optimization theory. Belmont, MA: Athena Scientific.

    Google Scholar 

  22. Boyd, S. P., & Vandenberghe, L. (2004). Convex optimization. Cambridge, MA: Cambridge University Press.

    Book  Google Scholar 

  23. Scutari, G., Palomar, D. P., & Barbarossa, S. (2008). Optimal linear precoding strategies for wideband noncooperative systems based on game theorypart I: Nash equilibria. IEEE Transactions on Signal Processing, 56(3), 1230–1249.

    Article  Google Scholar 

  24. Arrow, K. J., Hurwicz, L., Uzawa, H., & Chenery, H. B. (1958). Studies in linear and non-linear programming (Vol. 2). Stanford: Stanford University Press.

    Google Scholar 

  25. Nedi, A., & Ozdaglar, A. (2009). Subgradient methods for saddle-point problems. Journal of Optimization Theory and Applications, 142(1), 205–228.

    Article  Google Scholar 

  26. Shiu, D. S., Foschini, G. J., Gans, M. J., & Kahn, J. M. (2000). Fading correlation and its effect on the capacity of multielement antenna systems. IEEE Transactions on Communications, 48(3), 502–513.

    Article  Google Scholar 

  27. Musavian, L., Nakhai, M. R., Dohler, M., Aissa, S. (2006). Effect of channel uncertainty on the mutual information of MIMO multiple access channels. In: Proceedings of the Vehicular Technology Conference (VTC), (pp. 1–5). IEEE

  28. Tulino, A. M., Lozano, A., & Verdu, S. (2004). Power allocation in multiantenna communication with statistical channel information at the transmitter. In: Proceedings of the 15th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC, 2004, vol. 3. IEEE.

  29. Jafar, S. A., & Goldsmith, A. (2004). Transmitter optimization and optimality of beamforming for multiple antenna systems. IEEE Transactions on Wireless Communications, 3(4), 1165–1175.

    Article  Google Scholar 

  30. Rosen, J. B. (1965). Existence and uniqueness of equilibrium points for concave n-person games. Econometrica: Journal of the Econometric Society, 33(3), 520–534.

  31. Cover, T. M., & Thomas, A. (1988). Determinant inequalities via information theory. SIAM Journal on Matrix Analysis and Applications, 9(3), 384–392.

    Article  Google Scholar 

  32. Nash, J. F. (1950). Equilibrium points in n-points games. Proceedings of the National Academy of Science, 36(1), 48–49.

    Article  Google Scholar 

  33. Chiang, M., Low, S. H., Calderbank, A. R., & Doyle, J. C. (2007). Layering as optimization decomposition: A mathematical theory of network architectures. Proceedings of the IEEE, 95(1), 255–312.

    Article  Google Scholar 

  34. Dantzig, G. B., & Thapa, M. N. (2003). Linear programming 2: 2: Theory and extensions (vol. 2). New York: Springer.

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Tabriz, Emam Ave, 29 Bahman Blvd, Tabriz, Iran

    Samira Mir Mazhari Anvar, Sohrab Khanmohammadi & Javad Musevi niya

Authors
  1. Samira Mir Mazhari Anvar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sohrab Khanmohammadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Javad Musevi niya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Samira Mir Mazhari Anvar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mir Mazhari Anvar, S., Khanmohammadi, S. & Musevi niya, J. Game theoretic power allocation for fading MIMO multiple access channels with imperfect CSIR. Telecommun Syst 61, 875–886 (2016). https://doi.org/10.1007/s11235-015-0043-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11235-015-0043-4

Keywords

Search

Navigation