Generalized Analysis on Diversity-Multiplexing Trade-off of Relay Protocols

Under the more practical assumption that transmitters have no knowledge of the channel state information (CSI) but the channel distribution information (CDI), this paper examines the diversity-multiplexing trade-off (DMT) of two classes of cooperative protocols, namely, the amplify-and-forward (AF) and decode-and-forward (DF) protocols, with a three-node half-duplex relay network under slow fading. First, analyzing these protocols reveals that each one has its own optimal DMT with a specific time slot ratio, i.e., the ratio between the durations of the slots assigned to base station transmission and that assigned to relay transmission. We then demonstrate that under ideal coding, the incremental decode-and-forward protocol approaches the DMT upper bound when the two slots are of equal length, which outperforms all the other protocols. Furthermore, it is proved that the selective decode-and-forward protocol achieves its optimal performance with a slot assignment ratio of ( √ 5+ 1)/2. In addition, we also find AF, selective AF and incremental AF have no difference from the perspective of DMT.