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  • Research Article
  • Open Access

A Variational Approach to the Modeling of MIMO Systems

EURASIP Journal on Wireless Communications and Networking20072007:049350

  • Received: 17 February 2006
  • Accepted: 26 March 2007
  • Published:


Motivated by the study of the optimization of the quality of service for multiple input multiple output (MIMO) systems in 3G (third generation), we develop a method for modeling MIMO channel . This method, which uses a statistical approach, is based on a variational form of the usual channel equation. The proposed equation is given by with scalar variable . Minimum distance of received vectors is used as the random variable to model MIMO channel. This variable is of crucial importance for the performance of the transmission system as it captures the degree of interference between neighbors vectors. Then, we use this approach to compute numerically the total probability of errors with respect to signal-to-noise ratio (SNR) and then predict the numbers of antennas. By fixing SNR variable to a specific value, we extract informations on the optimal numbers of MIMO antennas.


  • Information System
  • Minimum Distance
  • Statistical Approach
  • Optimal Number
  • System Application


Authors’ Affiliations

Groupe Canal, Radio & Propagation, Lab/UFR-PHE, Faculté des Sciences, Rabat, Morocco
Virtual African Centre for Basic Science and Technology (VACBT), Focal Point Lab/UFR-PHE, Faculty of Sciences, Rabat, Morocco


  1. Love DJ, Heath RW Jr., Santipach W, Honig ML: What is the value of limited feedback for MIMO channels? IEEE Communications Magazine 2004,42(10):54-59. 10.1109/MCOM.2004.1341261View ArticleGoogle Scholar
  2. Gesbert D, Shafi M, Shiu D-S, Smith PJ, Naguib A: From theory to practice: an overview of MIMO space-time coded wireless systems. IEEE Journal on Selected Areas in Communications 2003,21(3):281-302. 10.1109/JSAC.2003.809458View ArticleGoogle Scholar
  3. Erceg V, Hari KVS, Smith MS, et al.: Channel models for fixed wireless applications. In Tech. Rep. IEEE 802.16-3c-01/29r4. The Communication Technology Laboratory, Zurich, Switzerland; 2001.Google Scholar
  4. Foschini GJ, Gans MJ: On limits of wireless communications in a fading environment when using multiple antennas. Wireless Personal Communications 1998,6(3):311-335. 10.1023/A:1008889222784View ArticleGoogle Scholar
  5. Proaki JG: Digital Communication. 3rd edition. McGraw-Hill, New York, NY, USA; 1995.Google Scholar
  6. Giorgetti A, Chiani M, Win MZ: The effect of narrowband interference on wideband wireless communication systems. IEEE Transactions on Communications 2005,53(12):2139-2149. 10.1109/TCOMM.2005.860047View ArticleGoogle Scholar
  7. Hirosaki B: An orthogonally multiplexed QAM system using the discrete Fourier transform. IEEE Transactions on Communications 1981,29(7):982-989. 10.1109/TCOM.1981.1095093View ArticleGoogle Scholar
  8. Mussardo G: Off-critical statistical models: factorized scattering theories and bootstrap program. Physics Report 1992,218(5-6):215-379. 10.1016/0370-1573(92)90047-4MathSciNetView ArticleGoogle Scholar
  9. Baym G: Lectures on Quantum Mechanics. W. A. Benjamin, New York, NY, USA; 1969.MATHGoogle Scholar
  10. Messiah A: Quantum Mechanics. Volume 2. Dunod, Paris, France; 1972.MATHGoogle Scholar
  11. Prasad R, Mohr W, Konhauser W: Third Generation Mobile Communication Systems. Artech House, Norwood, Mass, USA; 2000. Universal Personal Communications LibrarGoogle Scholar
  12. Winters JH: On the capacity of radio communication systems with diversity in a Rayleigh fading environment. IEEE Journal on Selected Areas in Communications 1987,5(5):871-878. 10.1109/JSAC.1987.1146600View ArticleGoogle Scholar
  13. Telatar IE: Capacity of multi-antenna Gaussian channels. European Transactions on Telecommunications 1999,10(6):585-595. 10.1002/ett.4460100604View ArticleGoogle Scholar
  14. 3GPP : Multiple-input multiple-output antenna processing for HSDPA. In Tech. Rep. 3GPP TR 25.876 v0.0.1. ARIB, CWTS, ETSI, TI, TTA, TTc, 650 Route des Luccoles-Sofia Antipolis, Valbonne, France; 2001:2001-2011.
  15. Burel G: Theoretical results for fast determination of the number of antennas in MIMO transmission systems. Proceedings of the IASTED International Conference on Communications, Internet, and Information Technology (CIIT '02), November 2002, St Thomas, Virgin Islands, USAGoogle Scholar
  16. Tarokh V, Seshadri N, Calderbank AR: Space-time codes for high data rate wireless communication: performance criterion and code construction. IEEE Transactions on Information Theory 1998,44(2):744-765. 10.1109/18.661517MathSciNetView ArticleMATHGoogle Scholar
  17. Colton DL, Kress R: Integral Equation Methods in Scattering Theory. John Wiley & Sons, New York, NY, USA; 1983.MATHGoogle Scholar
  18. Colton DL, Kress R: Inverse Acoustic and Electromagnetic Scattering Theory. 2nd edition. Springer, New York, NY, USA; 1998.View ArticleMATHGoogle Scholar
  19. Kirsch A: An Introduction to the Mathematical Theory of Inverse Problems. Springer, New York, NY, USA; 1996.View ArticleMATHGoogle Scholar
  20. Raghavan V, Sayeed AM: MIMO capacity scaling and saturation in correlated environments. Proceedings of IEEE International Conference on Communications (ICC '03), May 2003, Anchorage, Alaska, USA 5: 3006-3010.Google Scholar
  21. Debbah M, Muller RR: MIMO channel modeling and the principle of maximum entropy. IEEE Transactions on Information Theory 2005,51(5):1667-1690. 10.1109/TIT.2005.846388MathSciNetView ArticleMATHGoogle Scholar


© A. Jraifi and E. H. Saidi. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.