  Linear transceiving schemes between the relay and the destination have
recently attracted much interest in MIMO amplify-and-forward (AF) relaying
systems due to low implementation complexity. In this paper, we provide
comprehensive analysis on the diversity order of the linear zero-forcing (ZF)
and minimum mean squared error (MMSE) transceivers. Firstly, we obtain a
compact closed-form expression for the diversity-multiplexing tradeoff (DMT)
through tight upper and lower bounds. While our DMT analysis accurately
predicts the performance of the ZF transceivers, it is observed that the MMSE
transceivers exhibit a complicated rate dependent behavior, and thus are very
unpredictable via DMT for finite rate cases. Secondly, we highlight this
interesting behavior of the MMSE transceivers and characterize the diversity
order at all finite rates. This leads to a closed-form expression for the
diversity-rate tradeoff (DRT) which reveals the relationship between the
diversity, the rate, and the number of antennas at each node. Our DRT analysis
compliments our previous work on DMT, thereby providing a complete
understanding on the diversity order of linear transceiving schemes in MIMO AF
relaying channels.
