Finite-SNR Diversity-Multiplexing Tradeoff for Two-Way Multi-Antenna Relay Fading Channels

In this paper, we study the diversity-multiplexing tradeoff (DMT) of two-way relay channels (TWRC) with multi-antenna relay at finite signal-to-noise ratio (SNR). A two-phase decode-and-forward (DF) relay protocol and Rayleigh fading environment are considered. We first derive upper and lower bounds on the outage probability. These bounds are very tight for all practical SNR regions. Based on these bounds, the estimates of finite-SNR DMT (f-DMT) are then obtained. Our analysis shows that the multiplexing gain approaches one when SNR decreases to zero. On the other hand, the diversity gain approaches the number of relay antennas when SNR increases to infinity. Furthermore, the impact of time sharing, rate allocation and relay location on the outage and f-DMT is also discussed through numerical examples.