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

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.