Skip to main content

A General Theory for SIR Balancing

Abstract

We study the problem of maximizing the minimum signal-to-interference ratio (SIR) in a multiuser system with an adaptive receive strategy. The interference of each user is modelled by an axiomatic framework, which reflects the interaction between the propagation channel, the power allocation, and the receive strategy used for interference mitigation. Assuming that there is a one-to-one mapping between the QoS and the signal-to-interference ratio (SIR), the feasible QoS region is completely characterized by the max-min SIR balancing problem. In the first part of the paper, we derive fundamental properties of this problem for the most general case, when interference is modelled with an axiomatic framework. In the second part, we show more specific properties for interference functions based on a nonnegative coupling matrix. The principal aim of this paper is to provide a deeper understanding of the interaction between power allocation and interference mitigation strategies. We show how the proposed axiomatic approach is related to the matrix-based theory.

[1234567891011121314151617181920212223242526272829]

References

  1. Verdu S: Multiuser Detection. Cambridge University Press, Cambridge, UK; 1998.

    MATH  Google Scholar 

  2. Boche H, Stańczak S: Log-convexity of the minimum total power in CDMA systems with certain quality-of-service guaranteed. IEEE Transactions on Information Theory 2005,51(1):374–381. 10.1109/TIT.2004.839530

    Article  MathSciNet  MATH  Google Scholar 

  3. Boche H, Stańczak S: Convexity of some feasible QoS regions and asymptotic behavior of the minimum total power in CDMA systems. IEEE Transactions on Communications 2004,52(12):2190–2197. 10.1109/TCOMM.2004.838725

    Article  Google Scholar 

  4. Zander J, Kim S-L: Radio Resource Management for Wireless Networks. Artech House, Boston, Mass, USA; 2001.

    Google Scholar 

  5. Meyerhoff HJ: Method for computing the optimum power balance in multibeam satellites. COMSAT Technical Review 1974,4(1):139–146.

    Google Scholar 

  6. Aein JM: Power balancing in systems employing frequency reuse. COMSAT Technical Review 1973,3(2):277–299.

    Google Scholar 

  7. Boche H, Stańczak S: The infeasible SIR region is not a convex set. Proceedings of IEEE International Symposium on Information Theory (ISIT '05), September 2005, Adelaide, Australia 695–699.

    Google Scholar 

  8. Yates RD: A framework for uplink power control in cellular radio systems. IEEE Journal on Selected Areas in Communications 1995,13(7):1341–1347. 10.1109/49.414651

    Article  MathSciNet  Google Scholar 

  9. Yates RD, Ching-Yao H: Integrated power control and base station assignment. IEEE Transactions on Vehicular Technology 1995,44(3):638–644. 10.1109/25.406632

    Article  Google Scholar 

  10. Hanly SV: An algorithm for combined cell-site selection and power control to maximize cellular spread spectrum capacity. IEEE Journal on Selected Areas in Communications 1995,13(7):1332–1340. 10.1109/49.414650

    Article  Google Scholar 

  11. Farsakh C, Nossek JA: Spatial covariance based downlink beamforming in an SDMA mobile radio system. IEEE Transactions on Communications 1998,46(11):1497–1506. 10.1109/26.729394

    Article  Google Scholar 

  12. Rashid-Farrokhi F, Tassiulas L, Liu KJR: Joint optimal power control and beamforming in wireless networks using antenna arrays. IEEE Transactions on Communications 1998,46(10):1313–1324. 10.1109/26.725309

    Article  Google Scholar 

  13. Visotsky E, Madhow U: Optimum beamforming using transmit antenna arrays. Proceedings of 49th IEEE Vehicular Technology Conference (VTC '99), May 1999, Houston, Tex, USA 1: 851–856.

    Google Scholar 

  14. Bengtsson M, Ottersten B: Optimal and suboptimal transmit beamforming. In Handbook of Antennas in Wireless Communications. CRC Press, Boca Raton, Fla, USA; 2001. chapter 18

    Google Scholar 

  15. Schubert M, Boche H: Solution of the multi-user downlink beamforming problem with individual SINR constraints. IEEE Transactions on Vehicular Technology 2004,53(1):18-28.

    Article  Google Scholar 

  16. Wiesel A, Eldar YC, Shamai S: Linear precoding via conic optimization for fixed MIMO receivers. IEEE Transactions on Signal Processing 2006,54(1):161–176.

    Article  Google Scholar 

  17. Gerlach D, Paulraj A: Base station transmitting antenna arrays for multipath environments. Signal Processing 1996,54(1):59–73. 10.1016/0165-1684(96)00093-X

    Article  MATH  Google Scholar 

  18. Montalbano G, Slock DTM: Matched filter bound optimization for multiuser downlink transmit beamforming. Proceedings of IEEE International Conference on Universal Personal Communications (ICUPC '98), October 1998, Florence, Italy

  19. Schubert M, Boche H: A unifying theory for uplink and downlink multi-user beamforming. Proceedings of IEEE International Zurich Seminar on Broadband Communications, February 2002, Zurich, Switzerland 27–1-27–6.

  20. Boche H, Schubert M: Resource allocation for multi-antenna multi-user systems. Proceedings of IEEE International Conference on Communications (ICC '05), May 2005, Seoul, South Korea 2: 855–859.

  21. Boche H, Schubert M: Duality theory for uplink downlink multiuser beamforming. In Smart Antennas—State-of-the-Art, EURASIP Book Series. Hindawi, New York, NY, USA; 2006.

    Google Scholar 

  22. Gantmacher FR: The Theory of Matrices, Vol. 2. Chelsea, New York, NY, USA; 1959.

    MATH  Google Scholar 

  23. Boche H, Schubert M: On the structure of the unconstrained multiuser QoS region. to appear in IEEE Transactions on Signal Processing

  24. Schubert M, Boche H: A generic approach to QoS-based transceiver optimization. to appear in IEEE Transactions on Communications

  25. Schubert M, Boche H: Comparison of-norm and-norm optimization criteria for SIR-balanced multi-user beamforming. Signal Processing 2004,84(2):367–378. 10.1016/j.sigpro.2003.10.022

    Article  MATH  Google Scholar 

  26. Zander J: Performance of optimum transmitter power control in cellular radio systems. IEEE Transactions on Vehicular Technology 1992,41(1):57–62. 10.1109/25.120145

    Article  Google Scholar 

  27. Wielandt H: Unzerlegbare, nicht negative Matrizen. Mathematische Zeitschrift 1950, (52):642–648. and Mathematische Werke/Mathematical Works, Vol. 2, 100–106 de Gruyter, Berlin, 1996

  28. Seneta E: Non-Negative Matrices and Markov Chains. Springer, New York, NY, USA; 1981.

    Book  MATH  Google Scholar 

  29. Boche H, Wiczanowski M, Stańczak S: Unifying view on min-max-fairness, max-min fairness, and utility optimization in cellular networks. in preparation, 2006

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Martin Schubert.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Boche, H., Schubert, M. A General Theory for SIR Balancing. J Wireless Com Network 2006, 060681 (2006). https://doi.org/10.1155/WCN/2006/60681

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/WCN/2006/60681

Keywords