Effect of Geometry on the Diversity-Multiplexing Tradeoff in Relay Channels

We consider the diversity-multiplexing tradeoff in half duplex relay channels. In recent work by Azarian et al. [2], it was shown that Dynamic Decode and Forward (DDF) strictly dominates all the other schemes in the high SNR (HSNR) regime, with the inherent assumption that all the links have the same average SNR.. In this work, we introduce geometry into the problem by letting the SNR of different links scale differently with.. We exhaustively identify the tradeoff for DDF and Non-Orthogonal Amplify and Forward (NAF) when the SNRs are different. We show that, even when geometry is included, the dominance behavior of DDF still holds. In some regions, NAF can at most do as well as DDF. We also show that when the multiplexing gain exceeds the exponential order of the SNR of either source to relay or relay to destination channels, the tradeoff curve of DDF reduces to that of direct transmission.