Skip to content

Advertisement

  • Research Article
  • Open Access

Eigenstructures of MIMO Fading Channel Correlation Matrices and Optimum Linear Precoding Designs for Maximum Ergodic Capacity

EURASIP Journal on Advances in Signal Processing20072007:029749

https://doi.org/10.1155/2007/29749

  • Received: 27 October 2006
  • Accepted: 25 March 2007
  • Published:

Abstract

The ergodic capacity of MIMO frequency-flat and -selective channels depends greatly on the eigenvalue distribution of spatial correlation matrices. Knowing the eigenstructure of correlation matrices at the transmitter is very important to enhance the capacity of the system. This fact becomes of great importance in MIMO wireless systems where because of the fast changing nature of the underlying channel, full channel knowledge is difficult to obtain at the transmitter. In this paper, we first investigate the effect of eigenvalues distribution of spatial correlation matrices on the capacity of frequency-flat and -selective channels. Next, we introduce a practical scheme known as linear precoding that can enhance the ergodic capacity of the channel by changing the eigenstructure of the channel by applying a linear transformation. We derive the structures of precoders using eigenvalue decomposition and linear algebra techniques in both cases and show their similarities from an algebraic point of view. Simulations show the ability of this technique to change the eigenstructure of the channel, and hence enhance the ergodic capacity considerably.

Keywords

  • Correlation Matrice
  • Eigenvalue Distribution
  • Selective Channel
  • Ergodic Capacity
  • Channel Correlation

[12345678910111213141516171819]

Authors’ Affiliations

(1)
Department of Electrical and Computer Engineering, McGill University, 3480 University Street, Montréal, QC, H3A 2A7, Canada

References

  1. Chizhik D, Foschini GJ, Gans MJ, Valenzuela RA: Keyholes, correlations, and capacities of multi-element transmit and receive antennas. IEEE Transactions on Wireless Communications 2002,1(2):361-368. 10.1109/7693.994830View ArticleGoogle Scholar
  2. Gesbert D, Bölcskei H, Gore DA, Paulraj AJ: Outdoor MIMO wireless channels: models and performance prediction. IEEE Transactions on Communications 2002,50(12):1926-1934. 10.1109/TCOMM.2002.806555View ArticleGoogle Scholar
  3. Litva J, Lo TK: Digital Beamforming in Wireless Communications. Artech House, Boston, Mass, USA; 1996.Google Scholar
  4. Boukalov AO, Häggman SG: System aspects of smart-antenna technology in cellular wireless communications: an overview. IEEE Transactions on Microwave Theory and Techniques 2000,48(6):919-929. 10.1109/22.846718View ArticleGoogle Scholar
  5. Sampath H, Stoica P, Paulraj AJ: Generalized linear precoder and decoder design for MIMO channels using the weighted MMSE criterion. IEEE Transactions on Communications 2001,49(12):2198-2206. 10.1109/26.974266View ArticleGoogle Scholar
  6. Sampath H: Linear precoding and decoding for multiple input multiple output (MIMO) wireless channels, Ph.D. thesis. Stanford University, Stanford, Calif, USA; 2001.Google Scholar
  7. Scaglione A, Stoica P, Barbarossa S, Giannakis GB, Sampath H: Optimal designs for space-time linear precoders and decoders. IEEE Transactions on Signal Processing 2002,50(5):1051-1064. 10.1109/78.995062View ArticleGoogle Scholar
  8. Sampath H, Paulraj AJ: Linear precoding for space-time coded systems with known fading correlations. IEEE Communications Letters 2002,6(6):239-241. 10.1109/LCOMM.2002.1010867View ArticleGoogle Scholar
  9. Zhou S, Giannakis GB: Optimal transmitter eigen-beamforming and space-time block coding based on channel correlations. IEEE Transactions on Information Theory 2003,49(7):1673-1690. 10.1109/TIT.2003.813565MathSciNetView ArticleMATHGoogle Scholar
  10. Bahrami HR, Le-Ngoc T: Precoder design based on correlation matrices for MIMO systems. IEEE Transactions on Wireless Communications 2006,5(12):3579-3587.View ArticleGoogle Scholar
  11. Gesbert D, Bölcskei H, Gore DA, Paulraj AJ: Outdoor MIMO wireless channels: models and performance prediction. IEEE Transactions on Communications 2002,50(12):1926-1934. 10.1109/TCOMM.2002.806555View ArticleGoogle Scholar
  12. Telatar IE: Capacity of multi-antenna Gaussian channel. Bell Labs, Murray Hills, NJ, USA; 1995.Google Scholar
  13. 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
  14. Bölcskei H, Gesbert D, Paulraj AJ: On the capacity of OFDM-based spatial multiplexing systems. IEEE Transactions on Communications 2002,50(2):225-234.View ArticleGoogle Scholar
  15. Cover TM, Thomas JA: Elements of Information Theory. John Wiley & Sons, New York, NY, USA; 1991.View ArticleMATHGoogle Scholar
  16. Horn RA, Johnson CR: Matrix Analysis. Cambridge University Press, New York, NY, USA; 1985.View ArticleMATHGoogle Scholar
  17. Raleigh GG, Cioffi JM: Spatio-temporal coding for wireless communication. IEEE Transactions on Communications 1998,46(3):357-366. 10.1109/26.662641View ArticleGoogle Scholar
  18. Kafedziski V: Capacity of frequency selective fading channels with side information. Proceedings of the 32nd Asilomar Conference on Signals, Systems and Computers, November 1998, Pacific Grove, Calif, USA 2: 1758-1762.Google Scholar
  19. Liu K, Kadous T, Sayeed AM: Orthogonal time-frequency signaling over doubly dispersive channels. IEEE Transactions on Information Theory 2004,50(11):2583-2603. 10.1109/TIT.2004.836931MathSciNetView ArticleMATHGoogle Scholar

Copyright

© H. R. Bahrami and T. Le-Ngoc 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.

Advertisement