Design Criteria for Non-Orthogonal Space–Time Block Codes in Multipath Channels


We consider the problem of designing high rate space–time block codes in multipath fading channels. For this, both minimizing the effect of the self-interference induced by the code itself, and mitigating the inter-symbol-interference induced by the channel have to be addressed. We translate the problem into an equivalent problem of designing a constrained code in a single-path channel with more antennas, and argue that design criteria derived in single-path apply when optimizing this constrained code. Here we concentrate on an analytic measure pertinent to mutual information maximization and BER-performance optimization. The design program is successfully applied to rate one linear space–time transmissions from four transmit antennas. A family of discrete permutations of the transmitted sequences are considered. Performance is optimized within this family, and the results are seen to effect directly both mutual information and error performance.

Key words

Diversity multipath channels multiple antennas space–time block codes time-reversed codes. 


  1. 1.
    Tarokh V., Seshadri N., Calderbank A.R. (1998). Space–time codes for high data rate wireless communication: performance criterion and code construction. IEEE Transactions on Information Theory 44:744–765MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Alamouti S. (1998). A simple transmit diversity technique for wireless communications. IEEE Journal on Selected Areas in Communication 16:1451–1458CrossRefGoogle Scholar
  3. 3.
    Lindskog E., Paulraj A. (2000). A transmit diversity scheme for channels with intersymbol interference. IEEE International Conference on Communications (ICC) 1:307–311Google Scholar
  4. 4.
    Vook F.W., Thomas T.A. (2000) Transmit diversity schemes for broadband mobile communication systems. IEEE Vehicular Technology Conference 6:2523 – 2529 FallGoogle Scholar
  5. 5.
    Naguib A. (2001). On the matched filter bound of transmit diversity techniques. IEEE International Conference on Communications (ICC) 2:596 – 603Google Scholar
  6. 6.
    Zhou S., Giannakis G.B. (2001). Space–time coding with maximum diversity gains over frequency-selective faading channels. IEEE Signal Proceedings Letters 8(10):269 – 272CrossRefGoogle Scholar
  7. 7.
    Diggavi S.N., Al-Dhahir N., Calderbank A.R. (2003). Algebraic properties of space–time block codes in intersymbol interference multiple access channels. Transactions on Information Theory 49(10):2403–2414MathSciNetCrossRefGoogle Scholar
  8. 8.
    N. Al-Dhahir, Single-carrier frequency-domain equalization for space–time block-coded transmissions over broadband wireless channels, IEEE International Symposium on Personal, Indoor, and Mobile Radio Communication (PIMRC), pp. 143–146, 2001Google Scholar
  9. 9.
    Tarokh V., Jafarkhani H., Calderbank A.R. (1999) Space–time block codes from orthogonal designs. IEEE Transactions on Information Theory 45:1456–1467MATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    O. Tirkkonen, A. Boariu and A. Hottinen, Minimal non-orthogonal rate 1 space–time block code for 3 + Tx antennas, IEEE 6th International Symposium on Spread-Spectrum Techniques and Applications (ISSSTA), Vol. 2, pp. 429–432, 2000Google Scholar
  11. 11.
    Jafarkhani H. (2001). A quasi-orthogonal space–time block code. IEEE Transactions on Communications 49:1–4MATHCrossRefGoogle Scholar
  12. 12.
    O. Tirkkonen, Optimizing space–time block codes by constellation rotations, Finnish Wireless Communication Workshop, pp. 59–60, 2001.Google Scholar
  13. 13.
    Hassibi B., Hochwald B. (2002). High-rate codes that are linear in space and time. Transactions on Information Theory 48(7):1804–1824MATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Hottinen A., Tirkkonen O., Wichman R. (2003). Multiantenna Transceiver Techniques for 3G and Beyond. John Wiley and Sons, ChichesterCrossRefGoogle Scholar
  15. 15.
    El Gamal H., Damen M.O. (2003). Universal space–time coding. Transactions on Information Theory 49(5):1097–1119MATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    E. Lindskog and D. Flore, Time-reversal space–time block coding and transmit delay diversity-separate and combined, 34th Asilomar Conference on Signals, Systems and Computers, pp. 572–577, 2000Google Scholar
  17. 17.
    A. Hottinen and O. Tirkkonen, Precoder designs for high rate space–time block codes, Princeton Conference on Information Sciences and Systems (CISS), 2004Google Scholar
  18. 18.
    S. Iraji, O. Tirkkonen, A. Hottinen and K. Kuchi, Non-orthogonal space–time block code for multipath channel, IEEE International Symposium on Personal, Indoor, and Mobile Radio Communication (PIMRC), Vol. 4, pp. 2303–2307, 2004Google Scholar
  19. 19.
    O. Tirkkonen and R. Kashaev, Combined information and performance optimization of linear MIMO modulations, IEEE International Symposium on Informations Theory (ISIT), p. 76, July 2002Google Scholar
  20. 20.
    O. Tirkkonen and M. Kokkonen, Interference, information and performance in linear matrix modulation, IEEE International Symposium on Personal, Indoor, and Mobile Radio Communication (PIMRC), Vol. 1, pp. 27–32, September 2004Google Scholar
  21. 21.
    S. Sandhu and A. Paulraj, Space–time block codes: a capacity perspective, IEEE Communication Letters, Vol. 4, No. 12, December 2000Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1. HelsinkiFinland
  2. 2.Nokia Research CenterHelsinkiFinland

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