Outage Probability and Finite-SNR Diversity–Multiplexing Tradeoff for Two-Way Relay Fading Channels

In this paper, we analyze the outage probability and finite-SNR diversity-multiplexing tradeoff (f-DMT) performance for two-way relay channels (TWRCs). Both amplify-and-forward (AF) and decode-and-forward (DF) relay protocols are considered. The two source nodes are equipped with single antenna, and the relay is equipped with single or multiple antennas. First, we derive lower bounds of outage probability for single- and multiantenna relay AF, upper and lower bounds for multiantenna relay DF, and the exact closed-form expression for single-antenna DF. These results are suitable for arbitrary time-sharing and rate allocation for DF and arbitrary rate allocation for AF. Numerical results show that the derived lower bounds approximate very well the actual outage performance obtained by Monte Carlo simulation. Based on the tight lower bounds, we further derive estimates of the f-DMTs. We find that AF always outperforms DF in terms of f-DMT in all SNR regimes. However, the comparison result of outage performance between AF and DF depends on channel conditions. Finally, we also discuss the impact of relay location, time-sharing, and rate allocation on the outage and f-DMT via numerical examples.