Diversity-multiplexing tradeoff for the MIMO static half-duplex relay

In this work, we investigate the diversity-multiplexing tradeoff (DMT) of the multiple-antenna (MIMO) static half-duplex relay channel. The relay channel is assumed to be symmetric in terms of number of antennas, i.e. the source and the destination have n antennas each, and the relay has m antennas. A general expression is derived for the DMT upper bound, which can be achieved by a compress-and-forward protocol at the relay, under certain assumptions. It is observed that the static half-duplex DMT matches the full-duplex DMT when the relay has a single antenna, and is strictly below the full-duplex DMT when the relay has multiple antennas.