Advertisement

BER minimisation via optimal power allocation and eigenbeamforming in MIMO systems

  • Ricardo Tadashi Kobayashi
  • Alex Miyamoto Mussi
  • Taufik Abrão
Article
  • 24 Downloads

Abstract

In this contribution, the convex optimisation technique is deployed to optimize the data transmission in MIMO systems operating via eigenbeamforming. Initially, we study three optimal Power Allocation (PA) policies: the first one is used for maximising the total capacity, the equal power allocation and a PA proportional to the channel gains. In the sequence and more importantly, we propose a PA capable of minimising the average Bit Error Rate (BER) with a variable number of transmit antennas. In order to do so, the optimisation problem is first stated in the standard form; then the convexity of the problem will be proven; and finally, the optimisation problem is solved by using the Karush–Kuhn–Tucker conditions. Numerical results corroborate the analytic solution. Moreover, simulation results for both the average BER and sum capacity performance metrics demonstrate the effectiveness of the proposed beamforming MIMO power allocation schemes in terms of system capacity maximisation or alternatively the BER minimisation (reliability).

Keywords

MIMO systems Convex optimisation Lambert function KKT conditions Water-filling algorithm 

Notes

Acknowledgements

This work was supported in part by the National Council for Scientific and Technological Development (CNPq) of Brazil under Grant 304066/2015-0, Fundação Araucária under Grant 302/2012, and in part by State University of Londrina – Paraná State Government (UEL), and CAPES/DS scholarship.

References

  1. 1.
    Boyd, S., & Vandenberghe, L. (2004). Convex optimization. New York, NY: Cambridge University Press.CrossRefGoogle Scholar
  2. 2.
    Cho, K., & Yoon, D. (2002). On the general ber expression of one- and two-dimensional amplitude modulations. IEEE Transactions on Communications, 50(7), 1074–1080.CrossRefGoogle Scholar
  3. 3.
    Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J., & Knuth, D. E. (1996). On the Lambert w function. In Advances in computational mathematics (Vol. 5, pp. 329–360).Google Scholar
  4. 4.
    Dua, A., Medepalli, K., & Paulraj, A. J. (2006). Receive antenna selection in mimo systems using convex optimization. IEEE Transactions on Wireless Communications, 5(9), 2353–2357.CrossRefGoogle Scholar
  5. 5.
    Farrokhi, F. R., Lozano, A., Foschini, G. J., & Valenzuela, R. A. (2002). Spectral efficiency of fdma/tdma wireless systems with transmit and receive antenna arrays. IEEE Transactions on Wireless Communications, 1(4), 591–599.CrossRefGoogle Scholar
  6. 6.
    Goldsmith, A. (2005). Wireless communications. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  7. 7.
    Hampton, J. R. (2013). Introduction to MIMO communications. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  8. 8.
    Kalman, D. (1996). A singularly valuable decomposition: The SVD of a matrix. The College Mathematics Journal, 27(1), 2–23.CrossRefGoogle Scholar
  9. 9.
    Khalighi, M.-A., Brossier, J., Jourdain, G.V., & Raoof, K. (2001) Water filling capacity of Rayleigh MIMO channels. In 2001 12th IEEE international symposium on personal, indoor and mobile radio communications (Vol. 1, pp. A–155–A–158).Google Scholar
  10. 10.
    Lopes, W. T. A., Queiroz, W. J. L., Madeiro, F., & Alencar, M. S. (2007) Exact bit error probability of M-QAM modulation over flat Rayleigh fading channels. In Microwave and optoelectronics conference, 2007. IMOC 2007. SBMO/IEEE MTT-S international (pp. 804–806).Google Scholar
  11. 11.
    Molisch, A. F. (2010). Wireless communications. New York: Wiley.Google Scholar
  12. 12.
    Palomar, D. P., Bengtsson, M., & Ottersten, B. (2005). Minimum ber linear transceivers for MIMO channels via primal decomposition. IEEE Transactions on Signal Processing, 53(8), 2866–2882.CrossRefGoogle Scholar
  13. 13.
    Rappaport, T. S., Sun, S., Mayzus, R., Zhao, H., Azar, Y., Wang, K., et al. (2013). Millimeter wave mobile communications for 5G cellular: It will work!. Access IEEE, 1, 335–349.CrossRefGoogle Scholar
  14. 14.
    Ren, Z., Chen, S., Hu, B., & Ma, W. (2013). Proportional resource allocation with subcarrier grouping in ofdm wireless systems. IEEE Communications Letters, 17(5), 868–871.CrossRefGoogle Scholar
  15. 15.
    Roh, W., Seol, J.-Y., Park, J. H., Lee, B., Lee, J., Kim, Y., et al. (2014). Millimeter-wave beamforming as an enabling technology for 5G cellular communications: Theoretical feasibility and prototype results. Communications Magazine IEEE, 52(2), 106–113.CrossRefGoogle Scholar
  16. 16.
    Rusek, F., Persson, D., Lau, B. K., Larsson, E. G., Marzetta, T. L., Edfors, O., et al. (2012). Scaling up MIMO. IEEE Signal Processing Magazine, 30(1), 40–60.CrossRefGoogle Scholar
  17. 17.
    Staple, G., & Werbach, K. (2004). The end of spectrum scarcity. IEEE Spectrum, 41(3), 48–52.CrossRefGoogle Scholar
  18. 18.
    Telatar, E. (2008). Capacity of multi-antenna Gaussian channels. European Transactions on Telecommunications, 10(6), 585–595.CrossRefGoogle Scholar
  19. 19.
    Wolniansky, P. W., Foschini, G. J., Golden, G. D., & Valenzuela, R. (1998) V-BLAST: An architecture for realizing very high data rates over the rich-scattering wireless channel. In International symposium on signals, systems, and electronics, 1998. ISSSE 98. 1998 URSI (pp. 295–300).Google Scholar
  20. 20.
    Yang, P., Xiao, Y., Guan, Y. L., Hari, K. V. S., Chockalingam, A., Sugiura, S., et al. (2016). Single-carrier SM-MIMO: A promising design for broadband large-scale antenna systems. IEEE Communications Surveys and Tutorials, 18(3), 1687–1716.CrossRefGoogle Scholar
  21. 21.
    Zhang, Q., Jin, S., McKay, M., Morales-Jimenez, D., & Zhu, H. (2015). Power allocation schemes for multicell massive mimo systems. IEEE Transactions on Wireless Communications, 14(11), 5941–5955.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical Engineering (DEEL)State University of Londrina (UEL)LondrinaBrazil

Personalised recommendations