Skip to main content
Log in

Capacity of Generalized UTRA FDD Closed-Loop Transmit Diversity Modes

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

Transmit diversity techniques have received a lot of attention recently, and open-loop and closed-loop downlink transmit diversity modes for two transmit antennae have been included into universal terrestrial radio access (UTRA) frequency division duplex (FDD) specification. Closed-loop modes provide larger system capacity than open-loop modes, but they need additional side information of the downlink channel in the transmitter. In FDD systems this requires a separate feedback channel. Quantization of channel state information (CSI) in closed-loop transmit diversity schemes decreases the performance when compared to a closed-loop system where the transmitter has access to complete CSI. In this paper, we analyze the effect of quantization of CSI and deduce approximate capacity formulae for closed-loop transmit diversity schemes that are generalizations of the closed-loop schemes included in UTRA FDD specification. Moreover, we calculate approximation error and show by simulations that our approximation is tight for flat Rayleigh fading environments with and without fast transmit power control.

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. 3GPP. (2004). Physical layer procedures (FDD), 3GPP technical specification, TS 25.214, Ver. 6.4.0.

  2. Narula A., Lopez M., Trott M., Wornell G. (1998) Efficient use of side information in multiple-antenna data transmission over fading channels. IEEE Journal of Selected Areas on Communications, 16(8): 1423–1436

    Article  Google Scholar 

  3. Hämäläinen, J., & Wichman, R. (2000). Closed-loop transmit diversity for FDD WCDMA systems. In Proceedings of Asilomar conference on signals, systems and computers (Vol. 1, pp. 111–115).

  4. Hämäläinen, J., & Wichman, R. (2002). On the performance of FDD WCDMA closed-loop transmit diversity modes in Nakagami and Ricean fading channels. In Proceedings of the IEEE international symposium on spread spectrum techniques and applications (Vol. 1, pp. 24–28).

  5. Mukkavilli K., Sabharwal A., Erkip E., Aazhang B. (2003) On beamforming with finite rate feedback in multiple-antenna systems. IEEE Transactions on Information Theory 49(10): 2562–2579

    Article  MathSciNet  Google Scholar 

  6. Love D., Heath R., Strohmer T. (2003) Grassmannian beamforming for multiple-input multiple-output wireless systems IEEE Transactions on Information Theory 49(10): 2735–2747

    Article  Google Scholar 

  7. Hochwald B., Marzetta T., Richardson T., Sweldens W., Urbanke R. (2000) Systematic design of unitary space-time constellations. IEEE Transactions on Information Theory 46(6): 1962–1973

    Article  MATH  Google Scholar 

  8. Zhou S., Wang Z., Giannakis G. (2005) Quantifying the power loss when transmit beamforming relies on finite-rate feedback. IEEE Transactions on Wireless Communication 4(4): 1948–1957

    Article  Google Scholar 

  9. Au-Yeung C., Love D. (2007) On the performance of random vector quantization limited feedback beamforming in a MISO system. IEEE Transactions on Wireless Communication 6(2): 458–462

    Article  Google Scholar 

  10. Santipach W., Honig M. (2009) Capacity of a multiple-antenna fading channel with a quantized precoding matrix. IEEE Transactions on Information Theory 55(3): 1218–1234

    Article  MathSciNet  Google Scholar 

  11. Hämäläinen, J., & Wichman, R. (2002). Asymptotic bit error probabilities of some closed-loop transmit diversity schemes. In Proceedings of the IEEE global telecommunications conference (Vol. 1, pp. 360–364).

  12. Hämäläinen, J., & Wichman, R. (2001). Feedback schemes for FDD WCDMA systems in multipath environments. In Proceedings of the IEEE vehicular technology conference (Vol. 1, pp. 238–242).

  13. McEliece R., Stark W. (1984) Channels with block interference. IEEE Transactions on Information Theory 30(1): 44–53

    Article  MATH  Google Scholar 

  14. Hämäläinen, J., & Wichman, R. (2002). Performance analysis of closed-loop transmit diversity in the presence of feedback errors. In Proceedings of the IEEE international symposium on personal, indoor and mobile radio communications (Vol. 5, pp. 2297–2301).

  15. Onggosanusi E., Gatherer A., Dabak A., Hosur S. (2001) Performance analysis of closed-loop transmit diversity in the presence of feedback delay. IEEE Transactions on Communications 49(9): 1618–1630

    Article  MATH  Google Scholar 

  16. Choi J. (2002) Performance analysis for transmit antenna diversity with/without channel information. IEEE Transactions on Vehicular Technology 51(1): 101–113

    Article  Google Scholar 

  17. Heath, R., Jr., & Paulraj, A. (1998). A simple scheme for transmit diversity using partial channel feedback. In Proceedings of asilomar conference on signals, systems and computers, 2, 1073–1078.

  18. Alouini M.-S., Goldsmith A. (1999) of rayleigh fading channels under different adaptive transmission and diversity-combining techniques. IEEE Transactions on Vehicular Technology 48(4): 1165–1181

    Article  Google Scholar 

  19. Nakagami, M. (1958). The m-distribution—A general formula for intensity distribution of rapid fading. Statistical methods in radio wave propagation (pp. 581–635). New York, NTY, USA: McGraw-Hill.

  20. Jakes, W. (eds) (1974) Microwave mobile communications. Wiley, New York

    Google Scholar 

  21. Lieblein J. (1955) On moments of order statistics from the weibull distribution. Annals of Mathematical Statistics 26(2): 330–333

    Article  MATH  MathSciNet  Google Scholar 

  22. Abramowitz M., Stegun I. (1970) Handbook of mathematical functions. National Bureau of Standards, Washington, D.C

    Google Scholar 

  23. Gradshteyn I., Ryzhik I. (1965) Tables of integrals, series and products. Academic Press, New York

    Google Scholar 

  24. Goldsmith A., Varaiya P. (1997) Capacity of fading channels with channel side information. IEEE Transactions on Information Theory 43(6): 1986–1992

    Article  MATH  MathSciNet  Google Scholar 

  25. Cavers, J. (1999). Optimized use of diversity modes in transmitter diversity systems. In Proceedings of the IEEE vehicular technology conference (Vol. 3, pp. 1768–1773).

  26. Michalopoulos D., Lioumpas A., Karagiannidis G. (2008) Increasing power efficiency in transmitter diversity systems under error performance constraints. IEEE Transactions on Communications 56(12): 2025–2029

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Risto Wichman.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hämäläinen, J., Wichman, R., Dowhuszko, A.A. et al. Capacity of Generalized UTRA FDD Closed-Loop Transmit Diversity Modes. Wireless Pers Commun 54, 467–484 (2010). https://doi.org/10.1007/s11277-009-9735-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-009-9735-y

Keywords

Navigation