Finite-SNR Diversity-Multiplexing Tradeoff for Two-Way Relay Fading Channel

This paper studies the performance limits of two-way relay channel (TWRC) at finite signal-to-noise ratio (SNR) in Rayleigh fading environment. A two-phase decode-and-forward (DF) protocol is considered. We first derive closed-form expressions for both outage probability and diversity-multiplexing tradeoff (DMT). Our results are general and suitable for any time sharing and any rate allocation in the two-way relay protocol. It is found that DF outperforms amplify-and-forward (AF) when either multiplexing gain or SNR is small enough, otherwise, DF is inferior to AF in term of outage probability. Meanwhile, finite-SNR DMT of DF is always lower than that of AF regardless of SNR due to the additional sum-rate constraint imposed on the relay node for full decoding. Furthermore, the optimum relay location for any given combination of time sharing and rate allocation is presented.