  Diversity-multiplexing tradeoff (DMT) presents a compact framework to compare
various MIMO systems and channels in terms of the two main advantages they
provide (i.e. high data rate and/or low error rate). This tradeoff was
characterized asymptotically (SNR-> infinity) for i.i.d. Rayleigh fading
channel by Zheng and Tse [1]. The asymptotic DMT overestimates the finite-SNR
one [2]. In this paper, using the recent results on the asymptotic (in the
number of antennas) outage capacity distribution, we derive and analyze the
finite-SNR DMT for a broad class of channels (not necessarily Rayleigh fading).
Based on this, we give the convergence conditions for the asymptotic DMT to be
approached by the finite-SNR one. The multiplexing gain definition is shown to
affect critically the convergence point: when the multiplexing gain is defined
via the mean (ergodic) capacity, the convergence takes place at realistic SNR
values. Furthermore, in this case the diversity gain can also be used to
estimate the outage probability with reasonable accuracy. The multiplexing gain
definition via the high-SNR asymptote of the mean capacity (as in [1]) results
in very slow convergence for moderate to large systems (as 1/ln(SNR)^2) and,
hence, the asymptotic DMT cannot be used at realistic SNR values. For this
definition, the high-SNR threshold increases exponentially in the number of
antennas and in the multiplexing gain. For correlated keyhole channel, the
diversity gain is shown to decrease with correlation and power imbalance of the
channel. While the SNR-asymptotic DMT of Zheng and Tse does not capture this
effect, the size-asymptotic DMT does.
