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Wireless Networks

, Volume 21, Issue 5, pp 1537–1548 | Cite as

Characterising the Pareto frontier of multiple access rate region: a study on the effect of decoding order on achievable performance

  • S. Barman Roy
  • A. S. Madhukumar
Article

Abstract

For a multiple access channel, each user has its own power constraint. However, when a multiple access channel is being considered as the dual of a broadcast channel, it must exploit the additional freedom in power allocation and the constraint should be a sum power constraint. Duality helps us to transform the non-convex problems in a broadcast channel to convex problems in a multiple access channel. This helps to solve sum-rate optimisation problems with linear power constraints. However, maximising the sum-rate does not completely characterise the entire rate region boundary, formally called as the Pareto frontier. This work first reviews some of the existing results of polymatroid formulation from the Pareto optimality perspective and then proposes a complete characterisation of the Pareto frontier to show its relationship with the sum-rate optimisation problem. The significance of decoding order on the achievable rate region is considered. The work also shows some of the decoding orders to be suboptimal in Pareto sense and proposes an algorithm to find the correct decoding order based on power allocation. Simulation results are presented to support the theoretical arguments.

Keywords

Duality Interference management Multiple access channel Pareto optimality Resource allocation 

Notes

Acknowledgments

The work was supported by the Ministry of Education, Singapore Government Project Number RG42/12. The authors express their gratitude to editor Prof. Edmundo Monteiro and the reviewers for their advices to improve the work.

References

  1. 1.
    Annapureddy, V. S., & Veeravalli, V. V. (2009). Gaussian interference networks: Sum capacity in the low interference regime and new outer bounds on the capacity region. IEEE Transactions on Information Theory, 55(7), 3032–3050.MathSciNetCrossRefGoogle Scholar
  2. 2.
    Boche, H., & Schubert, M. (2008). A superlinearly and globally convergent algorithm for power control and resource allocation with general interference functions. IEEE/ACM Transactions on Networking, 16(2), 383–395. doi: 10.1109/TNET.2007.900362.CrossRefGoogle Scholar
  3. 3.
    Boyd, S., & Vandenberghe, L. (2004). Convex optimization (2nd ed.). New York: Cambridge University Press. doi: 10.1016/B978-012428751-8/50019-7.
  4. 4.
    Brehmer, J., Bai, Q., & Utschick, W. (2008). Time sharing solutions in MIMO broadcast channel utility maximization. In ITG Workshop on Smart Antennas (pp. 153–156). Wien.Google Scholar
  5. 5.
    Edmonds, J. (1969). Submodular functions, matroids, and certain polyhedra. In International Conference on Combinatorial Structures and Applications (pp. 69–87). Calgary. http://link.springer.com/chapter/10.1007/3-540-36478-1_2
  6. 6.
    Etkin, R. H., Tse, D. N. C., & Wang, H. (2008). Gaussian interference channel capacity to within one bit. IEEE Transactions on Information Theory, 54(12), 5534–5562.MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Fung, C. H. F., Yu, W., & Lim, T. J. (2007). Precoding for the multiantenna downlink : Multiuser SNR gap and optimal user ordering. IEEE Transactions on Communications, 55(1), 188–197.CrossRefGoogle Scholar
  8. 8.
    Goldsmith, A. J., Jafar, S. A., Jindal, N., & Vishwanath, S. (2003). Capacity limits of MIMO channels. IEEE Journal on Selected Areas in Communications, 21(5), 684–702.CrossRefGoogle Scholar
  9. 9.
    Grant, M. C. (2004). Disciplined convex programming. Ph.D. thesis, Stanford University. http://www.stanford.edu/boyd/papers/pdf/mcg_thesis
  10. 10.
    Huh, H., Papadopoulos, H., & Caire, G. (2009). MIMO broadcast channel optimization under general linear constraints. In International Symposium on Information Theory (pp. 2664–2668). Seoul. doi: 10.1109/ISIT.2009.5205911
  11. 11.
    Jafar, S. A., Foschini, G. J., & Goldsmith, A. J. (2004). PhantomNet: Exploring optimal multicellular multiple antenna systems. EURASIP Journal on Advances in Signal Processing (5), 591–604. doi: 10.1155/S1110865704312072. http://asp.eurasipjournals.com/content/2004/5/691857
  12. 12.
    Jindal, N., Vishwanath, S., & Goldsmith, A. J. (2004). On the duality of Gaussian multiple-access and broadcast channels. IEEE Transactions on Information Theory, 50(5), 768–783. doi: 10.1109/TIT.2004.826646.MATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Lindblom, J., Karipidis, E., & Larsson, E. G. (2013). Efficient computation of Pareto optimal beamforming vectors for the MISO interference channel with successive interference cancellation. IEEE Transactions on Signal Processing, 61(19), 4782–4795.MathSciNetCrossRefGoogle Scholar
  14. 14.
    Motahari, A. S., & Khandani, A. K. (2009). Capacity bounds for the Gaussian interference channel. IEEE Transactions on Information Theory, 55(2), 620–643.MathSciNetCrossRefGoogle Scholar
  15. 15.
    Schubert, M., & Boche, H. (2007). A generic approach to QoS-based transceiver optimization. IEEE Transactions on Communications, 55(8), 1557–1566.CrossRefGoogle Scholar
  16. 16.
    Telatar, E. (1999). Capacity of multi-antenna Gaussian channels. European Transactions on Telecommunications, 10(6), 585–595.CrossRefGoogle Scholar
  17. 17.
    Tse, D. N. C., & Hanly, S. V. (1998). Multiaccess fading channels-part I: Polymatroid structure, optimal resource allocation and throughput capacities. IEEE Transactions on Information Theory, 44(7), 2796–2815.MATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    Tse, D. N. C., & Viswanath, P. (2005). Fundamentals of wireless communication (1st ed.). New York: Cambridge University Press.MATHCrossRefGoogle Scholar
  19. 19.
    Vishwanath, S., Jindal, N., & Goldsmith, A. J. (2003). Duality, achievable rates, and sum-rate capacity of Gaussian MIMO broadcast channels. IEEE Transactions on Information Theory, 49(10), 2658–2668. doi: 10.1109/TIT.2003.817421.MATHMathSciNetCrossRefGoogle Scholar
  20. 20.
    Zhang, L., Zhang, R., Liang, Y. C., Xin, Y., & Poor, H. V. (2012). On Gaussian MIMO BC-MAC duality with multiple transmit covariance constraints. IEEE Transactions on Information Theory, 58(4), 2064–2078.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Computer EngineeringNanyang Technological UniversityJurong WestSingapore

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