Skip to main content
Springer Nature Link
Log in

An Expression for the Average Quantization Error

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

The quantization error for MIMO (multiple-input multiple-output) downlink channels is known to be the minimum of independent and identically distributed beta random variables. In this note, an exact expression is derived for the average quantization error. Computational issues relating to its correctness, usage and approximations are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

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

    Article  Google Scholar 

  2. Jindal N. (2006) MIMO broadcast channels with finite rate feedback. IEEE Transactions on Information Theory 52: 5045–5059

    Article  MathSciNet  Google Scholar 

  3. Jindal, N. (2006). A feedback reduction technique for MIMO broadcast channels. In Proceedings of the IEEE International Symposium on Information Theory, pp. 2699–2703, 2006 July.

  4. Jindal, N. (2008). Antenna combining for the MIMO downlink channel. IEEE Transactions on Wireless Communications (to appear).

  5. van Zwet, W. R. (1964). Convex transformations of random variables. Mathematical Center Tracts, volume 7. Amsterdam: Mathematisch Centrum.

  6. Exton H. (1978) Handbook of hypergeometric integrals: theory, applications, tables, computer programs. Halsted Press, New York

    MATH  Google Scholar 

  7. Arnold B.C., Balakrishnan N., Nagaraja H.N. (1992) A first course in order statistics. Wiley, New York

    MATH  Google Scholar 

  8. David H.A., Nagaraja H.N. (2003) Order Statistics (3rd ed). Wiley, New York

    MATH  Google Scholar 

  9. Gupta A.K., Nadarajah S. (2004) Handbook of Beta Distribution and its applications. Marcel Dekker, New York

    MATH  Google Scholar 

  10. Prudnikov A.P., Brychkov Y.A. Marichev O.I. (1986) Integrals and series (Vol 1). Gordon and Breach Science Publishers, Amsterdam

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Manchester, Manchester, M13 9PL, UK

    Saralees Nadarajah

Authors
  1. Saralees Nadarajah
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Saralees Nadarajah.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nadarajah, S. An Expression for the Average Quantization Error. Wireless Pers Commun 49, 575–585 (2009). https://doi.org/10.1007/s11277-008-9578-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-008-9578-y

Keywords