Diversity-multiplexing tradeoff and outage probability in MIMO relay channels

MIMO single-relay fading channels are studied, where the source and destination are equipped with multiple antennas and the relay has a single one. Compact closed-form expressions are obtained for the outage probability under i.i.d. and correlated Rayleigh-fading links. Insightful high-SNR approximations are derived, which show the impact of the number of antennas, correlation, relay noise, relaying protocol, etc. Diversity-multiplexing tradeoff (DMT) is obtained for a broad class of fading distributions, including, as special cases, Rayleigh, Rice, Nakagami, Weibull, which may be non-identical, spatially correlated and/or non-zero mean. The DMT is shown to depend not on a particular fading distribution, but rather on its polynomial behavior near zero. It turns out to be the same for the simple “amplify-and-forward” protocol and more complicated “decode-and-forward” one with capacity achieving codes, i.e. the full processing capability at the relay does not help to improve the DMT. However, we also emphasize significant difference between the SNR-asymptotic DMT and the finite-SNR outage performance: while the former is not improved by using an extra antenna on either side, the latter can be significantly improved and, in particular, an extra antenna can be traded-off for a full processing capability at the relay.