  This paper investigates the diversity order of the minimum mean squared error
(MMSE) based optimal transceivers in multiple-input multiple-output (MIMO)
amplify-and-forward (AF) relaying systems. While the diversity-multiplexing
tradeoff (DMT) analysis accurately predicts the behavior of the MMSE receiver
for the positive multiplexing gain, it turned out that the performance is very
unpredictable via DMT for the case of fixed rates, because MMSE strategies
exhibit a complicated rate dependent behavior. In this paper, we establish the
diversity-rate tradeoff performance of MIMO AF relaying systems with the MMSE
transceivers as a closed-form for all fixed rates, thereby providing a complete
characterization of the diversity order together with the earlier work on DMT.
