On Outage Analysis and Code Design for Correlated MIMO Fading Channels

The diversity-multiplexing tradeoff (DMT) captures in a succinct and elegant way the tradeoff between error probability and rate achieved by space-time coding in the high- SNR, high spectral efficiency regime, of MIMO quasi-static fading channels. We show that the DMT for Rayleigh and Rician fading MIMO channels with arbitrary full-rank correlation is identical to the case of i.i.d. Rayleigh fading. Previously known results for the case of full-rank Kronecker correlations are recovered as special cases of this result. Then, we argue that while the impact of correlation on capacity and error probability may be huge, the gain achieved by optimizing the input covariance matrix with respect to standard white input is essentially negligible. This observation motivates the use of standard space-time codes irrespective of the channel correlation, with possibly a rate-adaptation mechanism that allocates the rate according to the channel correlation, in order to meet the desired error probability target.