Skip to main content

On the Channel Capacity of Multiantenna Systems with Nakagami Fading


We discuss the channel capacity of multiantenna systems with the Nakagami fading channel. Analytic expressions for the ergodic channel capacity or its lower bound are given for SISO, SIMO, and MISO cases. Formulae for the outage probability of the capacity are presented. It is shown that the channel capacity could be increased logarithmically with the number of receive antennas for SIMO case; while employing 3–5 transmit antennas (irrespective of all other parameters considered herein) can approach the best advantage of the multiple transmit antenna systems as far as channel capacity is concerned for MISO case. We have shown that for a given SNR, the outage probability decreases considerably with the number of receive antennas for SIMO case, while for MISO case, the upper bound of the outage probability decreases with the number of transmit antennas when the transmission rate is lower than some value, but increases instead when the transmission rate is higher than another value. A critical transmission rate is identified.


  1. 1.

    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:1008889222784

    Article  Google Scholar 

  2. 2.

    Telatar E: Capacity of multi-antenna Gaussian channels. European Transactions on Telecommunications 1999, 10(6):585–595. see also Tech. Rep., AT&T Bell Labs., 1995 10.1002/ett.4460100604

    MathSciNet  Article  Google Scholar 

  3. 3.

    Jayaweera S, Poor HV: On the capacity of multi-antenna systems in the presence of Rician fading. Proceedings of IEEE 56th Vehicular Technology Conference (VTC '02), September 2002, Vancouver, BC, Canada 4: 1963–1967.

    Article  Google Scholar 

  4. 4.

    Nakagami M:The-distribution - a general formula of intensity distribution of rapid fading. In Statistical Methods in Radio Wave Propagation. Edited by: Hoffman WC. Pergamon, Oxford, UK; 1960:3–36.

    Google Scholar 

  5. 5.

    Cassioli D, Win MZ, Molisch AF: The ultra-wide bandwidth indoor channel: from statistical model to simulations. IEEE Journal on Selected Areas in Communications 2002, 20(6):1247–1257. 10.1109/JSAC.2002.801228

    Article  Google Scholar 

  6. 6.

    Roussas GG: A Course in Mathematical Statistics. 2nd edition. Academic Press, San Diego, Calif, USA; 1997.

    Google Scholar 

  7. 7.

    Gradshteyn IS, Ryzhik IM: Table of Integrals, Series and Products. Academic Press, New York, NY, USA; 1980. corrected and enlarged edition, prepared by A. Jeffrey

    Google Scholar 

  8. 8.

    Gallager RG: Information Theory and Reliable Communication. John Wiley & Sons, New York, NY, USA; 1968.

    Google Scholar 

  9. 9.

    Muirhead RJ: Aspects of Multivariate Statistical Theory. John Wiley & Sons, New York, NY, USA; 1982.

    Google Scholar 

  10. 10.

    Biglieri E, Proakis J, Shamai S: Fading channels: information-theoretic and communications aspects. IEEE Transaction on Information Theory 1998, 44(6):2619–2692. 10.1109/18.720551

    MathSciNet  Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Feng Zheng.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Zheng, F., Kaiser, T. On the Channel Capacity of Multiantenna Systems with Nakagami Fading. EURASIP J. Adv. Signal Process. 2006, 039436 (2006).

Download citation


  • Information Technology
  • Transmission Rate
  • Quantum Information
  • Fading Channel
  • Outage Probability