Skip to main content
Log in

A Domain Decomposition Approach for Preconditioning in Massive MIMO Systems

  • Research Article - Electrical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

In this work, we investigate devising efficient preconditioners for communication systems based on domain decomposition techniques. In particular, we focus on the uplink of a massive MIMO system and exploit the special structure of the channel cross-correlation matrix to derive improved preconditioners based on Schwarz preconditioning. Up to our knowledge, this is the first attempt to make use of domain decomposition techniques in the design of efficient preconditioners for communication systems. Two additive Schwarz preconditioners are investigated and tested within the context of cancelling inter-antenna interference in massive MIMO systems using two recently proposed parallel interference cancellation detectors. Simulation results reveal substantial improvement in convergence speed compared to the conventional Jacobi and block Jacobi preconditioning.

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.

Similar content being viewed by others

References

  1. Larsson, E.G.; Tufvesson, F.; Edfors, O.; Marzetta, T.L.: Massive MIMO for next generation wireless systems. IEEE Commun. Mag. 52(2), 186–195 (2014)

    Article  Google Scholar 

  2. Honig, M.L.: Advances in Multiuser Detection, Wiley Series in Telecommunications and Signal Processing. ISBN: 9780470473801, Publication Date: 19-08-2009

  3. Yang, S.; Hanzo, L.: Fifty years of MIMO detection: the road to large-scale MIMOs. IEEE Commun. Surv. Tutor. 17(4), 941–1988 (2015)

    Article  Google Scholar 

  4. Wu, M.; Yin, B.; Vosoughi, A.; Studer, C.; Cavallaro, J. R.; Dick, C.: Approximate matrix inversion for high throughput data detection in the large scale MIMO uplink. In: IEEE International Symposium on Circuits and Systems (ISCAS) (2013)

  5. Wu, M.; Yin, B.; Wang, G.; Dick, C.; Cavallaro, J.R.; Studer, C.: Large-scale MIMO detection for 3GPP LTE: algorithms and FPGA implementations. IEEE J. Sel. Top. Signal Process. 8(5), 916–929 (2014)

    Article  Google Scholar 

  6. Ancora, A.; Montalbano, G.; Slock, D.T.M.: Preconditioned iterative inter-carrier interference cancellation for OFDM reception in rapidly varying channels. In: Proceedings of the ICASSP, pp. 3066–3069 (2010)

  7. Bentrcia, A.; Alshebeili, S.: New linear PIC detectors based on non-monotone line-search techniques. Signal Process 92(12), 3085–3090, ISSN 0165-1684 (2012). https://doi.org/10.1016/j.sigpro.2012.06.019

  8. Benzi, Michele: Preconditioning techniques for large linear systems: a survey. J. Comput. Phys. 182(2), 418–477 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. Xhafa, F.; Pllana, S.: Programming Multi-core and Many-core Computing Systems: Wiley Series on Parallel and Distributed Computing. Wiley-Blackwell, New York (2014)

    Google Scholar 

  10. Korneev, V.G.; Langer, U.: Domain decomposition methods and preconditioning. Encycl. Comput. Mech. 1, 22 (2004)

    Google Scholar 

  11. Giraud, L.; Tuminaro, R. S.: Algebraic domain decomposition preconditioners. Technical Report ENSEEIHT-IRIT RT/APO/06/07, Oct (2006)

  12. Okrouhl’ık, M.: Numerical methods in computational mechanics, Institute of Thermomechanics, Prague 2008, Last revision 23 Jan 2012

  13. Gander, M.J.: Schwarz methods over the course of time. Electron. Trans. Numer. Anal. 31, 228–255 (2008)

    MathSciNet  MATH  Google Scholar 

  14. Griebel, M.; Oswald, P.: On the abstract theory of additive and multiplicative Schwarz algorithms. Numer. Math. 70(2), 163–180 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  15. Nabben, R.: Comparisons between multiplicative and additive Schwarz iterations in domain decomposition methods. Numer. Math. 95(1), 145–162 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  16. Bai, Zhong-Zhi: On the convergence of additive and multiplicative splitting iterations for systems of linear equations. J. Comput. Appl. Math. 154(1), 195–214 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  17. Theory, An Algebraic Schwarz: Technical Report CRPC-94-12. Applied Mathematics and CRPC, California Institute of Technology (1994)

  18. van Zelst, A.; Hammerschmidt, J.S.: A single coefficient spatial correlation model for multiple-input multiple-output (MIMO) radio channels. In: proceedings of the URSI XXVIIth General Assembly. Maastricht, The Netherlands: URSI (2002)

  19. Bentrcia, A.; Zerguine, Azzedine: A new linear group-wise parallel interference cancellation detector. Wirel. Pers. Commun. 49(1), 23–34 (2009)

    Article  Google Scholar 

  20. Saad, Y.: Iterative methods for sparse linear systems. SIAM (2003). https://doi.org/10.1137/1.9780898718003

  21. Smith, B.: Domain decomposition: Parallel multilevel methods for elliptic partial differential equations. Cambridge University Press, Cambridge (2004)

    Google Scholar 

  22. Mathew, T.P.A.: Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations, Vol. 61 of Lecture Notes in Computational Science and Engineering. Springer, Berlin (2008)

  23. Yu, T.; Xiao, Z.; Wong, M.D. F.: Efficient parallel power grid analysis via Additive Schwarz Method. In: ICCAD, pp. 399–406 (2012)

  24. C-Cai, X.; Sarkis, M.: A restricted additive Schwarz preconditioner for general sparse linear systems. SIAM J. Sci. Comput. 21, 792–797 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  25. Loisel, Sébastien; Nabben, Reinhard; Szyld, Daniel B.: On hybrid multigrid-Schwarz algorithms. J. Sci. Comput. 36(2), 165–175 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  26. Bentrcia, Abdelouahab; Alshebeili, Saleh: Competitive linear parallel interference cancellation detection based on monotone line-search techniques. IET Signal Process. 8(5), 521–529 (2014)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Abdelouahab Bentrcia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bentrcia, A. A Domain Decomposition Approach for Preconditioning in Massive MIMO Systems. Arab J Sci Eng 44, 1757–1767 (2019). https://doi.org/10.1007/s13369-017-2988-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-017-2988-y

Keywords

Navigation