On Finite-SNR Diversity-Multiplexing Tradeoff

Diversitymultiplexing 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 (2003). The SNR-asymptotic DMT overestimates the finite-SNR one (R. Narasimhan, 2006). In this paper, using the recent results on the size-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). Systems with unequal number of Tx and Rx antennas exhibit qualitatively-different behavior from those with equal number of antennas: while the size-asymptotic DMT of the latter converges to the SNR- asymptotic DMT as the SNR grows, that of the former does not. However, the size-asymptotic DMT does provide an accurate approximation of the true DMT at low to moderately-high SNR, even for modest number of antennas, and hence is complementary of the SNR-asymptotic DMT of Zheng and Tse. Combining these two, a new DMT is obtained that is accurate over the whole SNR range. A number of generic properties of the DMT that hold at any SNR, for any number of antennas (i.e. not only asymptotic, either in size or in SNR) and for any fading channel are given. In particular, we demonstrate that the linear interpolation of the DMT for fractional multiplexing gain in (Zheng and Tse 2003) does not hold at finite SNR. Extensive Monte-Carlo simulations validate the analysis and the conclusions.