On Outage Probability and Diversity-Multiplexing Tradeoff in MIMO Relay Channels

TL;DR

This paper provides analytical expressions and insights into outage probability and the diversity-multiplexing tradeoff in MIMO relay channels, highlighting the effects of correlation, antenna count, and relay protocols.

Contribution

It derives closed-form outage probability expressions and the SNR-asymptotic DMT for various fading distributions, revealing the limited impact of relay processing on DMT.

Findings

Correlation has negligible impact unless near full correlation.

Extra antennas do not improve asymptotic DMT but can enhance finite-SNR outage performance.

Full relay processing does not improve the asymptotic DMT.

Abstract

Fading MIMO relay channels are studied analytically, when the source and destination are equipped with multiple antennas and the relays have a single one. Compact closed-form expressions are obtained for the outage probability under i.i.d. and correlated Rayleigh-fading links. Low-outage approximations are derived, which reveal a number of insights, including the impact of correlation, of the number of antennas, of relay noise and of relaying protocol. The effect of correlation is shown to be negligible, unless the channel becomes almost fully correlated. The SNR loss of relay fading channels compared to the AWGN channel is quantified. The SNR-asymptotic 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, and is 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. There is however a 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. The results are extended to the multi-relay channels with selection relaying and typical outage events are identified.