Diversity-multiplexing tradeoff over correlated Rayleigh fading channels: A non-asymptotic analysis

Zouheir Rezki*, David Haccoun, François Gagnon, Wessam Ajib

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In this paper, we present a finite-signal-to-noise ratio (finite-SNR) framework to establish tight bounds on the diversity-multiplexing tradeoff of a multiple input multiple output (MIMO) system. We focus on a more realistic propagation environment where MIMO channel fading coefficients are correlated and where SNR values are finite. The impact of spatial correlation on the fundamental diversity-multiplexing tradeoff is investigated. We present tight lower bounds on the outage probability of both spatially uncorrelated and correlated MIMO channels. Using these lower bounds, accurate finite-SNR estimates of the diversity-multiplexing tradeoff are derived. These estimates allow to gain insight on the impact of spatial correlation on the diversity-multiplexing tradeoff at finite-SNR. As expected, the diversity-multiplexing tradeoff is severely degraded as the spatial correlation increases. For example, a MIMO system operating at a spectral efficiency of R bps/Hz and at an SNR of 5 dB in a moderately correlated channel, achieves a better diversity gain than a system operating at the same spectral efficiency and at an SNR of 10 dB in a highly correlated channel, when the multiplexing gain r is greater than 0.8. Another interesting point is that provided that the spatial correlation channel matrix is of full rank, the maximum diversity gain is not affected by the spatial correlation.

Original languageEnglish (US)
Pages (from-to)188-199
Number of pages12
JournalWireless Communications and Mobile Computing
Issue number2
StatePublished - Feb 2010


  • Diversity-multiplexing tradeoff
  • Finite SNR
  • MIMO systems
  • Outage probability
  • Spatial correlation

ASJC Scopus subject areas

  • Information Systems
  • Computer Networks and Communications
  • Electrical and Electronic Engineering


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